Multiplication, multiples & factors
Tables, multiples and factors
In this section you use your times tables — including the 7 times table — to work out multiples and factors of whole numbers.
What is a multiple?
A multiple of a number is the answer you get when you multiply it by a whole number. The multiples of 7 are 7, 14, 21, 28, 35, 42 ... You can count on in sevens to find them. 21 is a multiple of 7 because 3 × 7 = 21.
What is a factor?
A factor of a number divides into it exactly, with nothing left over. 4 and 6 are factors of 24 because 4 × 6 = 24. Factors come in pairs. The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
Using arrays to find factors
An array arranges objects in equal rows. You can arrange 24 pieces into different rectangles: 1 × 24, 2 × 12, 3 × 8 and 4 × 6. Each rectangle shows a factor pair, so this helps you find all the factors of a number.
Inverse operations
Multiplication and division are inverse operations — they undo each other. This means you can check a division fact with multiplication: 21 ÷ 7 = 3 because 3 × 7 = 21. It also tells you 21 is a multiple of 7, and that 7 is a factor of 21.
Products
The product is the answer when you multiply numbers together. The product of 4 and 3 is 12, because 4 × 3 = 12.
Worked examples
Finding multiples of 7
- Start at 7 and count on in sevens.
- 7, 14, 21, 28, 35 ...
- Each number is a multiple of 7.
Answer: The first five multiples of 7 are 7, 14, 21, 28, 35.
Finding all the factors of 24
- Look for pairs of numbers that multiply to make 24.
- 1 × 24, 2 × 12, 3 × 8, 4 × 6.
- List every number used, in order.
Answer: The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
Is 35 a multiple of 7?
- Try to make 35 from the 7 times table.
- 5 × 7 = 35.
- So 35 is a multiple of 7.
Answer: Yes — 35 is a multiple of 7.
Checking with inverse operations
- You know 21 ÷ 7 = 3.
- Check it with the inverse: 3 × 7 = 21.
- The multiplication matches, so the division is correct.
Answer: 21 ÷ 7 = 3, and 3 × 7 = 21 confirms it.
Finding a product
- The product means the answer to a multiplication.
- Multiply 4 and 3.
- 4 × 3 = 12.
Answer: The product of 4 and 3 is 12.
Where you see this in real life
- Sharing a bar of 24 chocolate pieces equally among people — the numbers that work are the factors of 24.
- Packing 50 apples into boxes with the same number in each box.
- Spotting arrays in real life, like eggs in a carton or windows on a building.
Key words
- Multiple
- The answer when you multiply a number by a whole number, such as 21 being a multiple of 7.
- Factor
- A number that divides into another number exactly, with no remainder.
- Array
- Objects arranged in equal rows and columns.
- Product
- The answer when you multiply numbers together.
- Inverse operations
- Operations that undo each other, like multiplication and division.