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Factor Family

Dive into the concept of factors through a family analogy, understand how to find factors, spot special pairs, and explore the application of this skill in math and daily life.

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Factor Family

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  1. Factor Family When asked to find all the factors of a number, I like to think of them as members of a family. The HEAD of the family is the number that you have to find factors of. Some rules apply – 1) There can only be ONE HEAD of the family; 2) Family members (factors) come in pairs; 3) Sometimes there are special pairs who are identical twins.

  2. Here is an example: Find all the factors of 40: 40 – (head of the family) What does factors mean? How did I work out the factors of 40? The factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40. I see

  3. Checking: 40 = 1 x 40 40 = 2 x 20 40 = 4 x 10 40 = 5 x 8 How many 1s go into 40? How many 2s go into 40? How many 3s go into 40?

  4. Here is another example: Find all the factors of 36: 36 – (head of the family) Are these all the factors of 36?

  5. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36 Some of the factors of 36 are very special. Can you spot them? Can you explain why they are special? 2 is a prime number; 3 is a prime number; 6 is a twin so it’s written once on the list.

  6. Is there something that you must remember to help you find the factors of any number? Exercise 1: Match the factors to their number. You can re-use any of the factors. Number 14 16 23 27 50 • Factors • 8 4 • 3 50 • 25 5 Are some missing?

  7. Exercise 2: Find all the factors of1. 15 5. 422. 18 6. 553. 25 7. 754. 28 8. 89 Are any of them special and Why?

  8. Exercise 3: Each number has something in common besides the number 1 as a factor. What is it? For example: Hint: Every number has this ‘type of a number’ as a factor. The factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40 The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36 The factors of 15 are 1, 3, 5 and 15 The factors of 11 are 1 and 11 Challenge: Can you create a number equation with this ‘type of a number’ to the number (head of the family) whose factors you are trying to find. Would your number equation work if this ‘type of a number’ is the same as the number (head of the family) whose factors you are trying to find?

  9. The skills used to find factors and know them is useful in other areas of mathematics, like – simplifying fractions, ratio and proportion. It helps to find solutions faster. In daily life you can use the same skill to help with money. Bank clerks use them all the time. Exercise 4: This is a coin bag used by banks to store coins. How many £1 coins can you place in this bag? How many £2 coins can you place in this bag? How many 50p coins can you place in this bag? How many 20p coins can you place in this bag? How many 10p coins can you place in this bag? How many 5p coins can you place in this bag? How many 2p coins can you place in this bag? How many 1p coins can you place in this bag?

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