Factors and multiples

In your book, Maths Mela (Chapter 13, Animal Jumps), numbers go into a box, get multiplied by a secret number, and come out as 28, 36, 48 and 72. The secret multiplier could be 1, 2 or 4. These numbers have special names.

When we multiply, the numbers we multiply are called factors, and the answer is called a multiple. Look at 3 × 5 = 15. Make an array of 3 rows with 5 squares in each row: that is 15 squares. So 3 and 5 are factors of 15, and 15 is a multiple of 3 and a multiple of 5.

One number can have many arrays. The book makes every array for 12: 3 rows of 4 (3 × 4 = 12), 2 rows of 6 (2 × 6 = 12), and 1 row of 12 (1 × 12 = 12). Each array gives us factors, so the factors of 12 are 1, 2, 3, 4, 6 and 12.

To find all the factors of a number, try to make every possible array for it. If a number of rows works with no squares left over, that number of rows is a factor. For 12, 5 rows does not work: 5 × 2 = 10 and 5 × 3 = 15, so 5 is not a factor of 12.