GCF of 84 and 105 (Greatest Common Factor)

"Greatest Common Factor" Calculator

Greatest Common Factor of

and

What is the Greatest Common Divisor of 84 and 105?

Answer

GCF of 84 and 105 is
21

(Twenty-one)

Finding GCF for 84 and 105 using all factors (divisors) listing

The first method to find GCF for numbers 84 and 105 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 105: 1, 3, 5, 7, 15, 21, 35, 105

So the Greatest Common Factor for 84 and 105 is 21

Finding GCF for 84 and 105 by Prime Factorization

The second method to find GCF for numbers 84 and 105 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 105: 3, 5, 7

As we can see there are Prime Factors common to both numbers: 3, 7

Now we need to multiply them to find GCF: 3 × 7 = 21

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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 105? (The answer is: 21). Select the first number (e.g. '84') and the second number (e.g. '105'). 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
84906
84917
84924
84933
84942
84951
849612
84971
849814
84993
841004
841011
841026
841031
841044
8410521
841062
841071
8410812
841091
841102
841113
8411228
841131
841146
841151
841164
841173
841182
841197

FAQ

What is the Greatest Common Divisor of 84 and 105?

GCF of 84 and 105 is 21

How to find the GCF of 84 and 105?

You can find the GCF of 84 and 105 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 84 and 105 is 21.

What prime factors do 84 and 105 share?

The prime factorizations of 84 and 105 have 3 × 7 in common, and multiplying those shared primes gives 21 — exactly the greatest common factor.

How does the GCF reduce the fraction 84/105?

Divide the numerator and the denominator by the GCF 21: 84 ÷ 21 = 4 and 105 ÷ 21 = 5. So 84/105 in lowest terms is 4/5.

See Also