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3 years ago

What is the GCF of 84 and 56

Mathematics

2 answers:

Elden [556K]3 years ago

8 0

Prime factorization for both numbers:

84 = 2*2*3*7

56= 2*2*2*7

prime factors: 2*2*7

answer: 28

vfiekz [6]3 years ago

6 0

Answer:

The GCF is 28

Step-by-step explanation:

<u>Step 1: Find the factors of both numbers</u>

84 → 1, 2 , 3 , 4 , 6 , 7 , 12 , 14 , 21 , 28 , 42 , 84

56 → 1 , 2 , 4 , 7 , 8 , 14 , 28 , 56

The factor that is the biggest common in both is the GCF. We see that 28 is the biggest factor that matches for both numbers.

Answer: The GCF is 28

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We start this case similarly to the previous one, we count how many subsets of 4 elements we can form from a set of n elements. The answer is the combinatorial number of n with 4 ${n \choose 4} .$

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As we did before, we pick 3 elements from a set of n. The amount of possibilities is ${n \choose 3} .$

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Case (4): 2 numbers are different

We pick 2 numbers from a set of n, with a total of ${n \choose 2}$ possibilities. We have 4 options to define the other 3 numbers, they can all three of them be equal to the biggest number, there can be 2 equal to the biggest number and 1 to the smallest one, there can be 1 equal to the biggest number and 2 to the smallest one, and they can all three of them be equal to the smallest number.