Numbers can be broken down and built up in fascinating...
Mathematics2 views·Na-update Jun 8, 2026·5 mga pahinaUnderstanding Factors, Multiples, and Prime Numbers
1 / 5
1
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Understanding the Key Terms
Factors are numbers that divide perfectly into another number with no remainder left over. Think of them as the building blocks hiding inside a number. When you're looking for factors, you're basically asking "what numbers can I multiply together to get this number?"
Multiples work the opposite way - they're what you get when you multiply a number by whole numbers like 1, 2, 3, and so on. It's just like reciting times tables! Multiples keep getting bigger and go on forever.
Prime numbers are the special ones that only have exactly two factors: 1 and themselves. They're like the VIPs of the number world because they can't be broken down any further.
💡 Remember: Factors divide INTO a number, multiples come FROM multiplying a number!
2
of 5
Finding Factors and Multiples
Finding factors is like detective work - you're hunting for pairs of numbers that multiply together to make your target number. Start with 1, then work your way up until you've found all the pairs. For example, with 12: you get 1×12, 2×6, and 3×4, giving you factors of 1, 2, 3, 4, 6, and 12.
Multiples are dead easy - just multiply your number by 1, 2, 3, 4, and keep going. The multiples of 7 are 7, 14, 21, 28, 35, and they continue forever.
Prime numbers have exactly two factors, no more and no less. The number 7 is prime because only 1 and 7 divide into it perfectly. Remember: 1 isn't prime (it only has one factor), and 2 is the only even prime number!
💡 Quick Check: If a number has more than two factors, it's called a composite number!
3
of 5
The Sieve Method and Finding HCF
The Sieve of Eratosthenes is a brilliant way to find all prime numbers up to any limit. You start with a grid of numbers, cross out 1, then systematically eliminate multiples of each prime you find. It's like a mathematical sieve that lets only the primes fall through!
Finding the Highest Common Factor (HCF) involves a simple three-step process. First, list all the factors of both numbers. Then identify which factors appear in both lists. Finally, pick the biggest one from your common factors.
For example, with 18 and 24: the factors of 18 are 1, 2, 3, 6, 9, 18, and the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The common factors are 1, 2, 3, 6, so the HCF is 6.
💡 Pro Tip: The HCF is always smaller than or equal to the smaller of your two numbers!
4
of 5
Finding LCM and Common Mistakes
The Lowest Common Multiple (LCM) is the smallest number that both your original numbers divide into perfectly. List the multiples of each number until you spot the first one that appears in both lists. With 8 and 10: multiples of 8 are 8, 16, 24, 32, 40... and multiples of 10 are 10, 20, 30, 40... so the LCM is 40.
The biggest mistake students make is mixing up factors and multiples! Factors are the few numbers that divide INTO your number, whilst multiples are the many numbers you get FROM multiplying. Think: factors are few, multiples are many.
Another common error is forgetting that 1 isn't a prime number. Prime numbers must have exactly two factors - 1 and themselves. Also, when finding HCF, make sure you list ALL the factors, not just the obvious ones.
💡 Memory Trick: HCF goes down (finding the highest factor), LCM goes up (finding the lowest multiple)!
5
of 5
Quick Test Summary
You've got the tools to tackle any factors, multiples, and primes question now! Factors divide into numbers exactly, multiples come from times tables, and prime numbers only have two factors: 1 and themselves.
For HCF, list all factors for each number, spot the common ones, then pick the biggest. For LCM, list multiples until you find the first match between your numbers.
The key to success is not mixing up factors and multiples - get this right and everything else falls into place. Remember that factors are the building blocks inside numbers, whilst multiples are what you build by multiplying outwards.
💡 Test Success: Practice identifying whether you need factors or multiples first - then the rest becomes straightforward!
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Mathematics2 views·Na-update Jun 8, 2026·5 mga pahinaUnderstanding Factors, Multiples, and Prime Numbers
Numbers can be broken down and built up in fascinating ways that'll help you tackle fractions and solve complex maths problems. Understanding factors, multiples, and prime numbers is like having a mathematical toolkit that makes everything else easier.
1
of 5
Mag-sign up para makita ang content. Libre ito!
- Access sa lahat ng dokumento
- Pagbutihin ang iyong mga grado
- Sumali sa milyong mga estudyante
Understanding the Key Terms
Factors are numbers that divide perfectly into another number with no remainder left over. Think of them as the building blocks hiding inside a number. When you're looking for factors, you're basically asking "what numbers can I multiply together to get this number?"
Multiples work the opposite way - they're what you get when you multiply a number by whole numbers like 1, 2, 3, and so on. It's just like reciting times tables! Multiples keep getting bigger and go on forever.
Prime numbers are the special ones that only have exactly two factors: 1 and themselves. They're like the VIPs of the number world because they can't be broken down any further.
💡 Remember: Factors divide INTO a number, multiples come FROM multiplying a number!
2
of 5Mag-sign up para makita ang content. Libre ito!
- Access sa lahat ng dokumento
- Pagbutihin ang iyong mga grado
- Sumali sa milyong mga estudyante
Finding Factors and Multiples
Finding factors is like detective work - you're hunting for pairs of numbers that multiply together to make your target number. Start with 1, then work your way up until you've found all the pairs. For example, with 12: you get 1×12, 2×6, and 3×4, giving you factors of 1, 2, 3, 4, 6, and 12.
Multiples are dead easy - just multiply your number by 1, 2, 3, 4, and keep going. The multiples of 7 are 7, 14, 21, 28, 35, and they continue forever.
Prime numbers have exactly two factors, no more and no less. The number 7 is prime because only 1 and 7 divide into it perfectly. Remember: 1 isn't prime (it only has one factor), and 2 is the only even prime number!
💡 Quick Check: If a number has more than two factors, it's called a composite number!
3
of 5Mag-sign up para makita ang content. Libre ito!
- Access sa lahat ng dokumento
- Pagbutihin ang iyong mga grado
- Sumali sa milyong mga estudyante
The Sieve Method and Finding HCF
The Sieve of Eratosthenes is a brilliant way to find all prime numbers up to any limit. You start with a grid of numbers, cross out 1, then systematically eliminate multiples of each prime you find. It's like a mathematical sieve that lets only the primes fall through!
Finding the Highest Common Factor (HCF) involves a simple three-step process. First, list all the factors of both numbers. Then identify which factors appear in both lists. Finally, pick the biggest one from your common factors.
For example, with 18 and 24: the factors of 18 are 1, 2, 3, 6, 9, 18, and the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The common factors are 1, 2, 3, 6, so the HCF is 6.
💡 Pro Tip: The HCF is always smaller than or equal to the smaller of your two numbers!
4
of 5Mag-sign up para makita ang content. Libre ito!
- Access sa lahat ng dokumento
- Pagbutihin ang iyong mga grado
- Sumali sa milyong mga estudyante
Finding LCM and Common Mistakes
The Lowest Common Multiple (LCM) is the smallest number that both your original numbers divide into perfectly. List the multiples of each number until you spot the first one that appears in both lists. With 8 and 10: multiples of 8 are 8, 16, 24, 32, 40... and multiples of 10 are 10, 20, 30, 40... so the LCM is 40.
The biggest mistake students make is mixing up factors and multiples! Factors are the few numbers that divide INTO your number, whilst multiples are the many numbers you get FROM multiplying. Think: factors are few, multiples are many.
Another common error is forgetting that 1 isn't a prime number. Prime numbers must have exactly two factors - 1 and themselves. Also, when finding HCF, make sure you list ALL the factors, not just the obvious ones.
💡 Memory Trick: HCF goes down (finding the highest factor), LCM goes up (finding the lowest multiple)!
5
of 5Mag-sign up para makita ang content. Libre ito!
- Access sa lahat ng dokumento
- Pagbutihin ang iyong mga grado
- Sumali sa milyong mga estudyante
Quick Test Summary
You've got the tools to tackle any factors, multiples, and primes question now! Factors divide into numbers exactly, multiples come from times tables, and prime numbers only have two factors: 1 and themselves.
For HCF, list all factors for each number, spot the common ones, then pick the biggest. For LCM, list multiples until you find the first match between your numbers.
The key to success is not mixing up factors and multiples - get this right and everything else falls into place. Remember that factors are the building blocks inside numbers, whilst multiples are what you build by multiplying outwards.
💡 Test Success: Practice identifying whether you need factors or multiples first - then the rest becomes straightforward!
Akala namin hindi mo na itatanong...
Ano ang Knowunity AI companion?
Ang aming AI Companion ay isang AI tool na nakatuon sa mga estudyante na nag-aalok ng higit pa sa mga sagot lang. Binuo mula sa milyong Knowunity resources, nagbibigay ito ng may-kaugnayang impormasyon, personalized na study plans, quizzes, at content direkta sa chat, na umaangkop sa iyong sariling learning journey.
Saan ko mada-download ang Knowunity app?
Maaari mong i-download ang app mula sa Google Play Store at Apple App Store.
Talaga bang libre ang Knowunity?
Tama 'yan! Mag-enjoy sa libreng access sa mga study content, makipag-connect sa kapwa mga estudyante, at kumuha ng instant na tulong – lahat nasa iyong daliri lang.
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6th Year1430
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Notes on mo ghrá-sa
5th Year380
IrishAn Gaeilge Aiste
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6th Year1320
Hindi mo mahanap ang hinahanap mo? Tuklasin ang iba pang mga asignatura.
Gustong-gusto kami ng mga estudyante — at magiging ganoon ka rin.
4.6/5App Store
4.7/5Google Play
Napakadaling gamitin at maganda ang disenyo ng app. Nahanap ko lahat ng hinahanap ko hanggang ngayon at natuto ako ng marami mula sa mga presentasyon! Tiyak na gagamitin ko ang app para sa isang takdang-aralin sa klase! At siyempre, nakakatulong din ito bilang inspirasyon.
Stefan Sgumagamit ng iOS
Sobrang ganda talaga ng app na ito. Maraming mga study notes at tulong [...]. Ang problemang subject ko ay Pranses, halimbawa, at ang app ay may maraming options para tumulong. Salamat sa app na ito, bumuti ang Pranses ko. Irerekumenda ko ito sa lahat.
Samantha KlichAndroid user
Wow, talagang namangha ako. Sinubukan ko lang ang app dahil nakita ko itong ina-advertise nang maraming beses at sobrang nagulat ako. Ang app na ito ang TULONG na gusto mo para sa paaralan at higit sa lahat, nag-aalok ito ng maraming bagay, tulad ng workouts at fact sheets, na SOBRANG nakatulong sa akin.
AnnaiOS user