Which expression shows (45 + 15) in the form a(b + c), where a is the greatest common factor of 45 and 15?
Responses
9(5 + 6)
9(5 + 6)
15(3 + 1)
15(3 + 1)
5(9 + 3)
5(9 + 3)
45(1 + 15)
The greatest common factor of 45 and 15 is 15. So we need to write (45 + 15) as 15 times the sum of two integers.
We can take out a factor of 15 from each term:
(45 + 15) = 15(3 + 1)
Therefore, the expression that shows (45 + 15) in the form a(b + c), where a is the greatest common factor of 45 and 15, is:
15(3 + 1)
So the correct answer is:
15(3 + 1)
To find the expression (45 + 15) in the form a(b + c), where a is the greatest common factor of 45 and 15, we need to find the greatest common factor (GCF) of 45 and 15 first.
The factors of 45 are 1, 3, 5, 9, 15, and 45.
The factors of 15 are 1, 3, 5, and 15.
To find the GCF, we need to find the largest number that appears in both factor lists. In this case, the GCF is 15.
Now that we have the GCF, we can express (45 + 15) as 15(3 + 1). Therefore, the expression that represents (45 + 15) in the form a(b + c), where a is the greatest common factor of 45 and 15, is 15(3 + 1).
To express (45 + 15) in the form a(b + c), where a is the greatest common factor of 45 and 15, we need to find the greatest common factor (GCF) of 45 and 15.
The factors of 45 are 1, 3, 5, 9, 15, and 45.
The factors of 15 are 1, 3, 5, and 15.
The only common factor of 45 and 15 is 15, so the GCF is 15.
Now we can rewrite the expression (45 + 15) as 15(3 + 1), where a = 15, b = 3, and c = 1.
Therefore, the expression that shows (45 + 15) in the form a(b + c), with a being the greatest common factor of 45 and 15, is:
15(3 + 1)