What is the Greatest Common Factor of 980 and 1000?

Greatest common factor (GCF) of 980 and 1000 is 20.

GCF(980,1000) = 20

We will now calculate the prime factors of 980 and 1000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 980 and 1000.

How to find the GCF of 980 and 1000?

We will first find the prime factorization of 980 and 1000. After we will calculate the factors of 980 and 1000 and find the biggest common factor number .

Step-1: Prime Factorization of 980

Prime factors of 980 are 2, 5, 7. Prime factorization of 980 in exponential form is:

980 = 2² × 5¹ × 7²

Step-2: Prime Factorization of 1000

Prime factors of 1000 are 2, 5. Prime factorization of 1000 in exponential form is:

1000 = 2³ × 5³

Step-3: Factors of 980

List of positive integer factors of 980 that divides 980 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490

Step-4: Factors of 1000

List of positive integer factors of 1000 that divides 980 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 980 and 1000. The biggest common factor number is the GCF number.
So the greatest common factor 980 and 1000 is 20.

Also check out the Least Common Multiple of 980 and 1000