Page 97 - Start Up Mathematics_4

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Factors and Multiples

Factors

We know that the numbers which are multiplied together to give a product are known as
factors of the product.
For example, 2 × 3 = 6 here 2 and 3 are the factors of 6.
The factors of a number divide the number completely without leaving a remainder.

For example, when we divide 6 by 2, the remainder is zero. So, 6 is exactly divisible by 2.
Thus, 2 is a factor of 6. Similarly, 3 is also a factor of 6.

Remember
On dividing a number by a smaller number, if the remainder is zero, then both
the divisor and the quotient are factors of the dividend.
Quotient
Factors of Divisor Dividend
dividend – Number
0 Remainder

We can find the factors of a number by multiplication or division.

Example 1: Write all the factors of 12.
Solution: By multiplication

Try 1 → 1 × 12 = 12, so 1 and 12 are factors
Try 2 → 2 × 6 = 12, so 2 and 6 are factors
Try 3 → 3 × 4 = 12, so 3 and 4 are factors

Try 4 → 4 × 3 = 12 → We will stop here since the factors are repeating.
So, the factors of 12 are 1, 2, 3, 4, 6 and 12.
Alternatively,

By division
Try 1 → 12 ÷ 1 = 12, so 1 and 12 are factors
Try 2 → 12 ÷ 2 = 6, so 2 and 6 are factors

Try 3 → 12 ÷ 3 = 4, so 3 and 4 are factors
Try 4 → 12 ÷ 4 = 3 → We will stop here since the factors are repeating.
So, the factors of 12 are 1, 2, 3, 4, 6 and 12.

Example 2: Write all the factors of 24.
Solution: Try 1 → 1 × 24 = 24, so 1 and 24 are factors

Try 2 → 2 × 12 = 24, so 2 and 12 are factors

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