How do you write the sum of the number 48+14 as the product of their GCF and another sum?

Question

Riley Anderson · Accepted Answer

#48+14 = 2xx31# #48 = color(red)(2)xx2xx2xx2xx3# #14 = color(red)(2)xx7# #=> "GCF"(14, 48) = 2# #48+14 = (2xx24) + (2xx7)# #=2xx(24+7)# #=2xx31#

Luna Angel · Answer

undefined To express the sum of two numbers, 48 and 14, as the product of their greatest common factor (GCF) and another sum, follow these steps:

1. Find the GCF of the two numbers, 48 and 14.
2. Divide each number by the GCF.
3. Rewrite the original sum using the GCF and the quotients obtained in step 2.

Let's proceed with the calculation:

1. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
   The factors of 14 are 1, 2, 7, and 14.
   The common factors are 1 and 2.
   Therefore, the GCF of 48 and 14 is 2.

2. Divide each number by the GCF:
   $ \frac{48}{2} = 24 $
   $ \frac{14}{2} = 7 $

3. Rewrite the original sum using the GCF and the quotients:
   $ 48 + 14 = 2 \times (24 + 7) $

So, the sum of 48 and 14 can be written as the product of their GCF (which is 2) and another sum, which is 24 + 7.