GCF of 84 and 112 (Greatest Common Factor)

"Greatest Common Factor" Calculator
Greatest Common Factor of
and

What is the Greatest Common Divisor of 84 and 112?

Answer

GCF of 84 and 112 is
28

(Twenty-eight)

Finding GCF for 84 and 112 using all factors (divisors) listing

The first method to find GCF for numbers 84 and 112 is to list all factors for both numbers and pick the highest common one:

All factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

All factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112

So the Greatest Common Factor for 84 and 112 is 28

Finding GCF for 84 and 112 by Prime Factorization

The second method to find GCF for numbers 84 and 112 is to list all Prime Factors for both numbers and multiply the common ones:

All Prime Factors of 84: 2, 2, 3, 7

All Prime Factors of 112: 2, 2, 2, 2, 7

As we can see there are Prime Factors common to both numbers: 2, 2, 7

Now we need to multiply them to find GCF: 2 × 2 × 7 = 28

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About "Greatest Common Factor" Calculator

This calculator will help you find the greatest common factor (GCF) of two numbers. For example, it can help you find out what is the Greatest Common Divisor of 84 and 112? (The answer is: 28). Select the first number (e.g. '84') and the second number (e.g. '112'). After that hit the 'Calculate' button.
Greatest Common Factor (GCF) also known as the Greatest Common Divisor (GCD) or Highest Common Factor (HCF) - it is the largest positive integer that divides each of the integers with zero remainder.
"Greatest Common Factor" Calculator
Greatest Common Factor of
and

GCF Table

Number 1Number 2GCF
84971
849814
84993
841004
841011
841026
841031
841044
8410521
841062
841071
8410812
841091
841102
841113
8411228
841131
841146
841151
841164
841173
841182
841197
8412012
841211
841222
841233
841244
841251
8412642

FAQ

What is the Greatest Common Divisor of 84 and 112?

GCF of 84 and 112 is 28

How to find the GCF of 84 and 112?

You can find the GCF of 84 and 112 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 84 and 112 is 28.

What prime factors do 84 and 112 share?

The prime factorizations of 84 and 112 have 2 × 2 × 7 in common, and multiplying those shared primes gives 28 — exactly the greatest common factor.

How does the GCF reduce the fraction 84/112?

Divide the numerator and the denominator by the GCF 28: 84 ÷ 28 = 3 and 112 ÷ 28 = 4. So 84/112 in lowest terms is 3/4.

See Also