GCF of 675 and 825 (Greatest Common Factor)

"Greatest Common Factor" Calculator
Greatest Common Factor of
and

What is the Greatest Common Divisor of 675 and 825?

Answer

GCF of 675 and 825 is
75

(Seventy-five)

Finding GCF for 675 and 825 using all factors (divisors) listing

The first method to find GCF for numbers 675 and 825 is to list all factors for both numbers and pick the highest common one:

All factors of 675: 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675

All factors of 825: 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825

So the Greatest Common Factor for 675 and 825 is 75

Finding GCF for 675 and 825 by Prime Factorization

The second method to find GCF for numbers 675 and 825 is to list all Prime Factors for both numbers and multiply the common ones:

All Prime Factors of 675: 3, 3, 3, 5, 5

All Prime Factors of 825: 3, 5, 5, 11

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

Now we need to multiply them to find GCF: 3 × 5 × 5 = 75

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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 675 and 825? (The answer is: 75). Select the first number (e.g. '675') and the second number (e.g. '825'). 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
675810135
6758111
6758121
6758133
6758141
6758155
6758163
6758171
6758181
6758199
6758205
6758211
6758223
6758231
6758241
67582575
6758261
6758271
6758289
6758291
6758305
6758313
6758321
6758331
6758343
6758355
6758361
67583727
6758381
6758391

FAQ

What is the Greatest Common Divisor of 675 and 825?

GCF of 675 and 825 is 75

How to find the GCF of 675 and 825?

You can find the GCF of 675 and 825 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 675 and 825 is 75.

What prime factors do 675 and 825 share?

The prime factorizations of 675 and 825 have 3 × 5 × 5 in common, and multiplying those shared primes gives 75 — exactly the greatest common factor.

How does the GCF reduce the fraction 675/825?

Divide the numerator and the denominator by the GCF 75: 675 ÷ 75 = 9 and 825 ÷ 75 = 11. So 675/825 in lowest terms is 9/11.

See Also