Question #a7661

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Answer 1 · 2017-08-25T11:35:05

See a solution process below:

First, let's find the GCG of the two numbers. Find the prime factors for each number as:

#49 = 7 xx 7#

#36 = 2 xx 7#

Now identify the common factors and determine the GCF:

#49 = color(red)(7) xx 7#

#36 = 2 xx color(red)(7)#

Therefore:

#"GCF" = color(red)(7)#

We can now write the sum as:

#49 + 14 => (color(red)(7) xx 7) + (color(red)(7) xx 2)#

We can factor the GCF out of each term giving:

#color(red)(7)(7 + 2)#

Answer 2 · 2017-08-29T13:16:42

#49+14=7xx9#

we can use the Euclidean Algorithm

#49=3xx14+7---(1)#

#14=2xx7+0---(2)#

the #GCF" "#is the last non zero remainder.

#GCF=7#

Now add #(1)" "&" "(2)#

#49+14=3xx14+7+2xx7#

#=>49+14=3xx14+3xx7#

take #7 " " #out as common factor on the #RHS#

#49+14=7(3xx2+3)#

#49+14=7xx9#