What is the Greatest Common Factor of 490 and 500?

Greatest common factor (GCF) of 490 and 500 is 10.

GCF(490,500) = 10

We will now calculate the prime factors of 490 and 500, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 490 and 500.

How to find the GCF of 490 and 500?

We will first find the prime factorization of 490 and 500. After we will calculate the factors of 490 and 500 and find the biggest common factor number .

Step-1: Prime Factorization of 490

Prime factors of 490 are 2, 5, 7. Prime factorization of 490 in exponential form is:

490 = 2¹ × 5¹ × 7²

Step-2: Prime Factorization of 500

Prime factors of 500 are 2, 5. Prime factorization of 500 in exponential form is:

500 = 2² × 5³

Step-3: Factors of 490

List of positive integer factors of 490 that divides 490 without a remainder.

1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245

Step-4: Factors of 500

List of positive integer factors of 500 that divides 490 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 490 and 500. The biggest common factor number is the GCF number.
So the greatest common factor 490 and 500 is 10.

Also check out the Least Common Multiple of 490 and 500