Using the GCF you found in Part B, rewrite 56 + 96 as two factors. One factor is the GCF and the other is the sum of two numbers that do not have a common factor. Show your work.
Answers
Answer:
56=2*2*2*7=2^3*7
96=2*2*2*2*2*3=2^5*3
56+96=2^3(7+2²*3)=8*(7+12)
Step-by-step explanation:
Answer:
The GCF( 56.96) is 8.
One factor is 8 and the other factor is 19 that do not have common factor.
Step-by-step explanation:
Given:
Rewrite the term 56+96 into two factor.
One factor of the given number is GCF(56,96)
To find: The GCF of 56,96 and the sum of two numbers that do not have a common factor.
Solution:
The given number is 56 and 96
Find the factors of 56.
⇒ 56 = 1, 2, 4, 7, 8, 14, 28, 56
Find the factors of 96:
⇒ 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
From the above factor we have the common term is 8.
Therefore the GCF of these 2 numbers is 8.
GCF(56 , 96) = 8
Given that rewrite given number as 56 + 96
⇒ 56 + 96 = 152
Find the factor of 152
The factors of 152 are:
⇒ 152 = 1, 2, 4, 8, 19, 38, 76, 152
Given that one factor is the GCF and other is the sum of two numbers
Therefore already we have GCF(56,96) is 8.
One factor is 8
Now We need to rewrite 152 as 2 factors, one of them is 8.
The other is the sum of 2 numbers that do not have a common factor.
The other factor is 19 because it is the sum of 10 and 9.
Factors of 10:
⇒10 = 1, 2, 5, 10
Factors of 9:
⇒ 9 = 1, 3, 9
From the above factor except 1, they do not have any common factors.
Therefore another factor is 19
⇒ 152 = 8 × 19
Hence one factor is 8 and other factor is 19
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