GCF of 45 and 75 (Greatest Common Factor)

"Greatest Common Factor" Calculator
Greatest Common Factor of
and

What is the Greatest Common Divisor of 45 and 75?

Answer

GCF of 45 and 75 is
15

(Fifteen)

Finding GCF for 45 and 75 using all factors (divisors) listing

The first method to find GCF for numbers 45 and 75 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 75: 1, 3, 5, 15, 25, 75

So the Greatest Common Factor for 45 and 75 is 15

Finding GCF for 45 and 75 by Prime Factorization

The second method to find GCF for numbers 45 and 75 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 75: 3, 5, 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 75? (The answer is: 15). Select the first number (e.g. '45') and the second number (e.g. '75'). 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
456015
45611
45621
45639
45641
45655
45663
45671
45681
45693
45705
45711
45729
45731
45741
457515
45761
45771
45783
45791
45805
45819
45821
45831
45843
45855
45861
45873
45881
45891

FAQ

What is the Greatest Common Divisor of 45 and 75?

GCF of 45 and 75 is 15

How to find the GCF of 45 and 75?

You can find the GCF of 45 and 75 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 45 and 75 is 15.

What prime factors do 45 and 75 share?

The prime factorizations of 45 and 75 have 3 × 5 in common, and multiplying those shared primes gives 15 — exactly the greatest common factor.

How does the GCF reduce the fraction 45/75?

Divide the numerator and the denominator by the GCF 15: 45 ÷ 15 = 3 and 75 ÷ 15 = 5. So 45/75 in lowest terms is 3/5.

See Also