Question

Tasha believes that she can rewrite the difference 120 − 84 as a product of the GCF of the two numbers and another difference. Is she correct? Complete the explanation. She is not correct. The GCF of 120 and 84 is 12 . So 120 − 84 can be written as 12 × 10 − × , which is × (10 − ) or × = .

Answer 1

Explanation:

GCF is greatest common factor. It is also termed as HCF.

Firstly we write the factors of 120 and 84

120 = 2×2×3×5×2

84 = 2×2×3×7

HCF of 120 and 84 = 12

ATQ,

Tasha believes that she can rewrite the difference 120 − 84 as a product of the GCF of the two numbers and another difference. Let's try to write like this.

120-84 = (12×10-12×7) [using the distributive property]

= 12(10-7)

It means that the difference 120 − 84 as a product of the GCF (i.e. 12) of the two numbers and another difference (i.e. 10-7). Hence, she is correct.