GCF of 180 and 420 (Greatest Common Factor)

"Greatest Common Factor" Calculator
Greatest Common Factor of
and

What is the Greatest Common Divisor of 180 and 420?

Answer

GCF of 180 and 420 is
60

(Sixty)

Finding GCF for 180 and 420 using all factors (divisors) listing

The first method to find GCF for numbers 180 and 420 is to list all factors for both numbers and pick the highest common one:

All factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

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 180 and 420 is 60

Finding GCF for 180 and 420 by Prime Factorization

The second method to find GCF for numbers 180 and 420 is to list all Prime Factors for both numbers and multiply the common ones:

All Prime Factors of 180: 2, 2, 3, 3, 5

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, 5

Now we need to multiply them to find GCF: 2 × 2 × 3 × 5 = 60

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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 180 and 420? (The answer is: 60). Select the first number (e.g. '180') 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
18040545
1804062
1804071
18040812
1804091
18041010
1804113
1804124
1804131
18041418
1804155
1804164
1804173
1804182
1804191
18042060
1804211
1804222
1804239
1804244
1804255
1804266
1804271
1804284
1804293
18043010
1804311
18043236
1804331
1804342

FAQ

What is the Greatest Common Divisor of 180 and 420?

GCF of 180 and 420 is 60

How to find the GCF of 180 and 420?

You can find the GCF of 180 and 420 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 180 and 420 is 60.

What prime factors do 180 and 420 share?

The prime factorizations of 180 and 420 have 2 × 2 × 3 × 5 in common, and multiplying those shared primes gives 60 — exactly the greatest common factor.

How does the GCF reduce the fraction 180/420?

Divide the numerator and the denominator by the GCF 60: 180 ÷ 60 = 3 and 420 ÷ 60 = 7. So 180/420 in lowest terms is 3/7.

See Also