GCF of 75 and 200 (Greatest Common Factor)

"Greatest Common Factor" Calculator
Greatest Common Factor of
and

What is the Greatest Common Divisor of 75 and 200?

Answer

GCF of 75 and 200 is
25

(Twenty-five)

Finding GCF for 75 and 200 using all factors (divisors) listing

The first method to find GCF for numbers 75 and 200 is to list all factors for both numbers and pick the highest common one:

All factors of 75: 1, 3, 5, 15, 25, 75

All factors of 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200

So the Greatest Common Factor for 75 and 200 is 25

Finding GCF for 75 and 200 by Prime Factorization

The second method to find GCF for numbers 75 and 200 is to list all Prime Factors for both numbers and multiply the common ones:

All Prime Factors of 75: 3, 5, 5

All Prime Factors of 200: 2, 2, 2, 5, 5

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

Now we need to multiply them to find GCF: 5 × 5 = 25

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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 75 and 200? (The answer is: 25). Select the first number (e.g. '75') and the second number (e.g. '200'). 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
751855
751863
751871
751881
751893
751905
751911
751923
751931
751941
7519515
751961
751971
751983
751991
7520025
752013
752021
752031
752043
752055
752061
752073
752081
752091
7521015
752111
752121
752133
752141

FAQ

What is the Greatest Common Divisor of 75 and 200?

GCF of 75 and 200 is 25

How to find the GCF of 75 and 200?

You can find the GCF of 75 and 200 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 75 and 200 is 25.

What prime factors do 75 and 200 share?

The prime factorizations of 75 and 200 have 5 × 5 in common, and multiplying those shared primes gives 25 — exactly the greatest common factor.

How does the GCF reduce the fraction 75/200?

Divide the numerator and the denominator by the GCF 25: 75 ÷ 25 = 3 and 200 ÷ 25 = 8. So 75/200 in lowest terms is 3/8.

See Also