What is the Greatest Common Factor of 476 and 490?

Greatest common factor (GCF) of 476 and 490 is 14.

GCF(476,490) = 14

We will now calculate the prime factors of 476 and 490, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 476 and 490.

How to find the GCF of 476 and 490?

We will first find the prime factorization of 476 and 490. After we will calculate the factors of 476 and 490 and find the biggest common factor number .

Step-1: Prime Factorization of 476

Prime factors of 476 are 2, 7, 17. Prime factorization of 476 in exponential form is:

476 = 2² × 7¹ × 17¹

Step-2: 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-3: Factors of 476

List of positive integer factors of 476 that divides 476 without a remainder.

1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238

Step-4: Factors of 490

List of positive integer factors of 490 that divides 476 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 476 and 490. The biggest common factor number is the GCF number.
So the greatest common factor 476 and 490 is 14.

Also check out the Least Common Multiple of 476 and 490