GCF of 84 and 420 (Greatest Common Factor)

"Greatest Common Factor" Calculator
Greatest Common Factor of
and

What is the Greatest Common Divisor of 84 and 420?

Answer

GCF of 84 and 420 is
84

(Eighty-four)

Finding GCF for 84 and 420 using all factors (divisors) listing

The first method to find GCF for numbers 84 and 420 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 420: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420

So the Greatest Common Factor for 84 and 420 is 84

Finding GCF for 84 and 420 by Prime Factorization

The second method to find GCF for numbers 84 and 420 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 420: 2, 2, 3, 5, 7

As we can see there are Prime Factors common to both numbers: 2, 2, 3, 7

Now we need to multiply them to find GCF: 2 × 2 × 3 × 7 = 84

Related Calculations

See Also

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 420? (The answer is: 84). Select the first number (e.g. '84') and the second number (e.g. '420'). 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
844053
8440614
844071
8440812
844091
844102
844113
844124
844137
844146
844151
844164
844173
844182
844191
8442084
844211
844222
844233
844244
844251
844266
844277
844284
844293
844302
844311
8443212
844331
8443414

FAQ

What is the Greatest Common Divisor of 84 and 420?

GCF of 84 and 420 is 84

How to find the GCF of 84 and 420?

You can find the GCF of 84 and 420 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 84 and 420 is 84.

What prime factors do 84 and 420 share?

The prime factorizations of 84 and 420 have 2 × 2 × 3 × 7 in common, and multiplying those shared primes gives 84 — exactly the greatest common factor.

How does the GCF reduce the fraction 84/420?

Divide the numerator and the denominator by the GCF 84: 84 ÷ 84 = 1 and 420 ÷ 84 = 5. So 84/420 in lowest terms is 1/5.

See Also