GCF of 45 and 60 (Greatest Common Factor)

"Greatest Common Factor" Calculator
Greatest Common Factor of
and

What is the Greatest Common Divisor of 45 and 60?

Answer

GCF of 45 and 60 is
15

(Fifteen)

Finding GCF for 45 and 60 using all factors (divisors) listing

The first method to find GCF for numbers 45 and 60 is to list all factors for both numbers and pick the highest common one:

All factors of 45: 1, 3, 5, 9, 15, 45

All factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

So the Greatest Common Factor for 45 and 60 is 15

Finding GCF for 45 and 60 by Prime Factorization

The second method to find GCF for numbers 45 and 60 is to list all Prime Factors for both numbers and multiply the common ones:

All Prime Factors of 45: 3, 3, 5

All Prime Factors of 60: 2, 2, 3, 5

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

Now we need to multiply them to find GCF: 3 × 5 = 15

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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 45 and 60? (The answer is: 15). Select the first number (e.g. '45') and the second number (e.g. '60'). 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
454545
45461
45471
45483
45491
45505
45513
45521
45531
45549
45555
45561
45573
45581
45591
456015
45611
45621
45639
45641
45655
45663
45671
45681
45693
45705
45711
45729
45731
45741

FAQ

What is the Greatest Common Divisor of 45 and 60?

GCF of 45 and 60 is 15

How to find the GCF of 45 and 60?

You can find the GCF of 45 and 60 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 45 and 60 is 15.

What prime factors do 45 and 60 share?

The prime factorizations of 45 and 60 have 3 × 5 in common, and multiplying those shared primes gives 15 — exactly the greatest common factor.

How does the GCF reduce the fraction 45/60?

Divide the numerator and the denominator by the GCF 15: 45 ÷ 15 = 3 and 60 ÷ 15 = 4. So 45/60 in lowest terms is 3/4.

See Also