The question is find the common factors of 12x, 36
When we solve it ; 12x =2×3×2×(×)
36=2×3×2×3
Common factors 2 , 2 and 3 then why fo we multiply the these numbers
*in my book the answer is 2×2×3 =6
( the question says common factors not hcf )
Sounds like the instructions were not too clear.
If it asks for the common factors, then I would list
{2,3,4,6} as any of those is a common factor. Now the HIGHEST common factor of those is 6.
To find the common factors of 12x and 36, we need to identify the numbers that divide evenly into both 12x and 36.
First, let's factorize 12x and 36:
12x = 2 × 2 × 3 × x
36 = 2 × 2 × 3 × 3
As you correctly noted, the common factors are 2, 2, and 3. However, when we multiply these numbers together, we get 2 × 2 × 3 = 12. So the product of the common factors is 12, not 6.
If you are looking for the greatest common factor (GCF) or highest common factor (HCF), which is the largest number that divides evenly into both 12x and 36, then the answer would indeed be 6. However, the question specifically asks for the common factors, not the GCF or HCF.
In this case, the common factors of 12x and 36 are 2, 2, and 3, and their product is 12.