i have to find the gcf of two numbers then rewrite the sum using the distributive property and i dont know what to do.

Question

i have 4. 

a) 42 + 14

 

b) 36 + 27

 

c) 16 + 72

 

d) 44 + 33

Answer 1

One way to find the GCF (Greatest Common Factor) of two numbers is to consider their prime factors:

   The prime factors of 14 are 2 and 7.

        Thus, all the factors of 14 are 1, 2, 7, 14.

   The prime factors of 42 are 2, 3, and 7.

        Thus, all the factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42

       (note: multiply all groupings of the primes)

 

Those lists are in ascending order, so we just find the Greatest (largest) --  it is 14.

 

Since the GCF is also Common, we may use the Distributive Property of Multiplication Over Addition:

     a(b+c) = ab + ac

   in reverse:

     ab + ac = a(b+c)

     42 + 14 = 14(3+1)                    a=14, b=3, c=1

 

Use what you've learned to conquer the others !!

Answer 2

a). 42 = (2)(21) = (2)(3)(7)

 

     14 = (2)(7)

 

     GCF = (2)(7) = 14

 

     So, 42 + 14 = (14)(3) + (14)(1) = 14(3 + 1) = 14(4) = 56

 

Do parts b, c, and d in a similar manner.