GCF of 315 and 180 (Greatest Common Factor)

"Greatest Common Factor" Calculator

Greatest Common Factor of

and

What is the Greatest Common Divisor of 315 and 180?

Answer

GCF of 315 and 180 is
45

(Forty-five)

Finding GCF for 315 and 180 using all factors (divisors) listing

The first method to find GCF for numbers 315 and 180 is to list all factors for both numbers and pick the highest common one:

All factors of 315: 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315

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

So the Greatest Common Factor for 315 and 180 is 45

Finding GCF for 315 and 180 by Prime Factorization

The second method to find GCF for numbers 315 and 180 is to list all Prime Factors for both numbers and multiply the common ones:

All Prime Factors of 315: 3, 3, 5, 7

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

As we can see there are Prime Factors common to both numbers: 3, 3, 5

Now we need to multiply them to find GCF: 3 × 3 × 5 = 45

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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 315 and 180? (The answer is: 45). Select the first number (e.g. '315') and the second number (e.g. '180'). 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
31516515
3151661
3151671
31516821
3151691
3151705
3151719
3151721
3151731
3151743
31517535
3151761
3151773
3151781
3151791
31518045
3151811
3151827
3151833
3151841
3151855
3151863
3151871
3151881
31518963
3151905
3151911
3151923
3151931
3151941

FAQ

What is the Greatest Common Divisor of 315 and 180?

GCF of 315 and 180 is 45

How to find the GCF of 315 and 180?

You can find the GCF of 315 and 180 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 315 and 180 is 45.

What prime factors do 315 and 180 share?

The prime factorizations of 315 and 180 have 3 × 3 × 5 in common, and multiplying those shared primes gives 45 — exactly the greatest common factor.

How does the GCF reduce the fraction 315/180?

Divide the numerator and the denominator by the GCF 45: 315 ÷ 45 = 7 and 180 ÷ 45 = 4. So 315/180 in lowest terms is 7/4.

See Also