GCF of 100 and 1000 (Greatest Common Factor)

"Greatest Common Factor" Calculator
Greatest Common Factor of
and

What is the Greatest Common Divisor of 100 and 1000?

Answer

GCF of 100 and 1000 is
100

(One hundred)

Finding GCF for 100 and 1000 using all factors (divisors) listing

The first method to find GCF for numbers 100 and 1000 is to list all factors for both numbers and pick the highest common one:

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

All factors of 1000: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000

So the Greatest Common Factor for 100 and 1000 is 100

Finding GCF for 100 and 1000 by Prime Factorization

The second method to find GCF for numbers 100 and 1000 is to list all Prime Factors for both numbers and multiply the common ones:

All Prime Factors of 100: 2, 2, 5, 5

All Prime Factors of 1000: 2, 2, 2, 5, 5, 5

As we can see there are Prime Factors common to both numbers: 2, 2, 5, 5

Now we need to multiply them to find GCF: 2 × 2 × 5 × 5 = 100

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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 100 and 1000? (The answer is: 100). Select the first number (e.g. '100') and the second number (e.g. '1000'). 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
10031010
1003155
10032020
1003355
1003455
10035050
1003555
10036020
10037010
10037525
10038020
10039010
1003955
100400100
10041010
1004155
10042020
10042525
10043010
1004355
10044020
1004455
1004555
10046020
10047010
10047525
10048020
1004855
100500100
1001000100

FAQ

What is the Greatest Common Divisor of 100 and 1000?

GCF of 100 and 1000 is 100

How to find the GCF of 100 and 1000?

You can find the GCF of 100 and 1000 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 100 and 1000 is 100.

What prime factors do 100 and 1000 share?

The prime factorizations of 100 and 1000 have 2 × 2 × 5 × 5 in common, and multiplying those shared primes gives 100 — exactly the greatest common factor.

How does the GCF reduce the fraction 100/1000?

Divide the numerator and the denominator by the GCF 100: 100 ÷ 100 = 1 and 1000 ÷ 100 = 10. So 100/1000 in lowest terms is 1/10.

See Also