Answer:
D. 12(3+4)
Step-by-step explanation:
You want the expression 36 +48 written using the greatest common factor and the distributive property.
The greatest common factor of 36 and 48 is the largest integer that divides both of them evenly. One way to look for that is to look at the difference of the numbers. If that divides both numbers, it is the GCF.
48 -36 = 12
48/12 = 4
36/12 = 3
The GCF in this instance is 12. Factoring that from both numbers, we can rewrite the sum as ...
36 +48 = 12(3 +4) . . . . . . matches choice D.
__
Additional comment
Technically, we have used Euclid's algorithm to find the GCF. That method looks at the remainder from division of the larger number by the smaller number: 48/36 = 1 r 12. Then the remainder replaces the larger number: 36/12 = 3 r 0. When the remainder is 0, the smaller number is the GCF.
Alternatively, you can factor each number to primes, and identify the largest set of factors that are common to both.
36 = 2·2·3·3
48 = 2·2·2·2·3
GCF = 2·2·3 = 12
Doing it this way, the numbers inside parentheses are the "left over" factors after the greatest common factor has been factored out:
36 +48 = 2·2·3(3 +2·2) = 12(3 +4)
