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Q5 Use prime factors to find the lowest number that divides exactiy by Dotn Q6 One day, Arran divides his action figures into equal groups of 26 . The next day, he divides them up into equal groups of 12 . Use prime factors to find the lowest possible number af action figures he owns. Q7 Jess goes swimming every 21 days. Seamus goes swimming every 35 days. They both went swimming today. Use prime factors to find the number of days it will be until they both go swimming on the same day again. Q8 a) Write 30,140 and 210 as products of their prime factors. b) Hence find the HCF of 30,140 and 210. Q9 a) Write 121,280 and 550 as products of their prime factors. b) Hence find the LCM of 121,280 and 550 . Q10 Use prime factors to find (i) the HCF and (ii) the LCM of each of the following sets of numbers. a) 65,143 and 231 b) 175,245 and 1225 c) 104,338 and 1078 Q11 a) Use prime factors to find a pair of numbers that have \( H C F=12 \) and \( L C M=120 \). b) Use prime factors to find a pair of numbers that have \( H C F=20 \) and \( L C M=300 \). Section 1 Arithmetic, Multiples and Factors

Ask by Bernard Salazar. in the United Kingdom
Mar 13,2025

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**Simplified Answers:** 1. **Q5:** Cannot determine the number without clarification on "Dotn." 2. **Q6:** Arran owns **156** action figures. 3. **Q7:** Jess and Seamus will swim together again in **105 days**. 4. **Q8a:** - \( 30,140 = 2^8 \times 5 \times 13 \times 233 \) - \( 210 = 2 \times 3 \times 5 \times 7 \) 5. **Q8b:** The HCF of 30,140 and 210 is **10**. 6. **Q9a:** - \( 121,280 = 2^8 \times 5 \times 19 \) - \( 550 = 2 \times 5^2 \times 11 \) 7. **Q9b:** The LCM of 121,280 and 550 is \( 2^8 \times 5^2 \times 11 \times 19 \). 8. **Q10a:** - HCF: **1** - LCM: \( 3 \times 5 \times 7 \times 11 \times 13 \) 9. **Q10b:** - HCF: **35** - LCM: **1225** 10. **Q10c:** - HCF: **26** - LCM: \( 2^3 \times 7 \times 13^2 \) 11. **Q11a:** - One possible pair is **12 and 120**. 12. **Q11b:** - One possible pair is **20 and 300**. **Summary:** - **Q5:** Cannot determine without clarification. - **Q6:** 156 action figures. - **Q7:** 105 days. - **Q8:** 30,140 = \( 2^8 \times 5 \times 13 \times 233 \), 210 = \( 2 \times 3 \times 5 \times 7 \), HCF = 10. - **Q9:** 121,280 = \( 2^8 \times 5 \times 19 \), 550 = \( 2 \times 5^2 \times 11 \), LCM = \( 2^8 \times 5^2 \times 11 \times 19 \). - **Q10:** - a) HCF = 1, LCM = \( 3 \times 5 \times 7 \times 11 \times 13 \) - b) HCF = 35, LCM = 1225 - c) HCF = 26, LCM = \( 2^3 \times 7 \times 13^2 \) - **Q11:** - a) Pair with HCF=12 and LCM=120: 12 and 120 - b) Pair with HCF=20 and LCM=300: 20 and 300

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In mathematics, prime factorization enables us to break down numbers into their simplest building blocks—prime numbers! For instance, the number 30,140 can be factored down to \(2^2 \times 5 \times 7 \times 43\), while 210 factors to \(2 \times 3 \times 5 \times 7\). This breakdown helps us find the greatest common factor (HCF) and least common multiple (LCM) by identifying shared primes! When working with prime factors, a common mistake is forgetting to check all factors when finding the HCF and LCM. It's essential to remember that the HCF is found by multiplying the smallest powers of all common prime factors, while the LCM is calculated by taking the highest powers. Be sure to keep your factors organized and double-check your math to avoid any boo-boos!

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