What is the Greatest Common Factor of 490 and 496?

Greatest common factor (GCF) of 490 and 496 is 2.

GCF(490,496) = 2

We will now calculate the prime factors of 490 and 496, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 490 and 496.

How to find the GCF of 490 and 496?

We will first find the prime factorization of 490 and 496. After we will calculate the factors of 490 and 496 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 496

Prime factors of 496 are 2, 31. Prime factorization of 496 in exponential form is:

496 = 2⁴ × 31¹

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 496

List of positive integer factors of 496 that divides 490 without a remainder.

1, 2, 4, 8, 16, 31, 62, 124, 248

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 490 and 496. The biggest common factor number is the GCF number.
So the greatest common factor 490 and 496 is 2.

Also check out the Least Common Multiple of 490 and 496