Answer:
The answer is 6(7 + 12) ⇒ 1st answer
Step-by-step explanation:
* Lets explain how to solve the problem
- Factors are the numbers you multiply together to get another number
- Ex: 4 × 5 = 20 ⇒ 4 and 5 are the factors of 20
- Factors of a number n are the numbers that can multiplied together
to give the number n
- Ex: The factors of 6 are 1 , 2 , 3 , 6 because 1 × 6 = 6 and 2 × 3 = 6
- The distributive property lets you multiply a sum by multiplying each
term separately and then add the products
- Ex: a(b + c) = ab + ac
* Lets solve the problem
- We want to find the greatest common factor in 42 + 72
∵ 42 = 1 × 42 , 2 × 21 , 3 × 14 , 6 × 7
∴ The factors of 42 are 1 , 2 , 3 , 6 , 7 , 14 , 21 , 42
∵ 71 = 1 × 72 , 2 × 36 , 3 × 24 , 4 × 18 , 6 × 12 , 8 × 9
∴ The factors of 72 are 1 , 2 , 3 , 4 , 6 , 8 , 9 , 12 , 18 , 24 , 36 , 72
- The common factors between 42 and 72 are the bold numbers
∵ The common factors between 42 and 72 are 1 , 2 , 3 , 6
∵ The greatest one of them is 6
∴ The greatest common factor of 42 and 72 is 6
- In the distributive property we have a number multiplying by a sum
of two numbers
∵ 42 ÷ 6 = 7 and 72 ÷ 6 = 12
- We can write 42 + 72 as 6 × 7 + 6 × 12 and take 6 as a common factor
∵ 42 + 72 = 6 × 7 + 6 × 12
- Take 6 as a common factor
∴ 42 + 72 = 6(7 + 12)
