Prime Factor Decomposition - Worded Problems PDF

Prime Factor Decomposition - Worded Problems This is a non-calculator exercise 1. Lane strikes her drum every 9 seconds and Rory plucks her guitar every 15 seconds. They strike and pluck at the same time at the beginning of the song. After how many seconds will they next strike and pluck...

Prime Factor Decomposition - Worded Problems This is a non-calculator exercise 1. Lane strikes her drum every 9 seconds and Rory plucks her guitar every 15 seconds. They strike and pluck at the same time at the beginning of the song. After how many seconds will they next strike and pluck together? 2. David has a length of ribbon which is 180cm long. Kylie’s length of ribbon is 225cm long. They want to cut the longest lengths of ribbon they can from their lengths without wasting any, and in such a way that every piece of ribbon they cut is equal in length. How long will the lengths be? 3. Express 960 as the product of prime factors. Use your result to show that 15 is the largest odd factor of 960. 4. The children at Freeferal Primary School are going on a school trip to Blackpool and every pupil who wants to attend must pay to do so. Mr N Rooly collects £255 from his pupils. Mrs K Ottick collects £136 from her pupils. If the cost is a whole number of pounds, what is the highest it could be? 5. The highest common factor of two numbers is 32. The lowest common multiple of the two numbers is 640. What could the two numbers be? 6. Cain washes his bedding every 4 weeks. Chas washes her bedding every 5 days. If they both wash their bedding on April 1st, what is the next date they will both wash their bedding? 7. By expressing it as the product of prime factors, show that 5625 is a square number. 8. Use prime factorisation to show that 27 000 is a cube number and find its cube root. 9. Sue-Lynn buys some packets of biscuits; each contains the same number of biscuits. She opens the packets up and counts the biscuits. She has 209 biscuits. How many packets could she have bought? 10. What is the smallest number that is divisible by 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 and 10? 11. For any number, m, m! is the product of all positive whole numbers from m itself down to 1. For example, 4! = 4 × 3 × 2 × 1. If n! = 28 × 34 × 52 × 7, find the value of n.