What is the Greatest Common Factor of 490 and 504?

Greatest common factor (GCF) of 490 and 504 is 14.

GCF(490,504) = 14

We will now calculate the prime factors of 490 and 504, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 490 and 504.

How to find the GCF of 490 and 504?

We will first find the prime factorization of 490 and 504. After we will calculate the factors of 490 and 504 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 504

Prime factors of 504 are 2, 3, 7. Prime factorization of 504 in exponential form is:

504 = 2³ × 3² × 7¹

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 504

List of positive integer factors of 504 that divides 490 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 490 and 504. The biggest common factor number is the GCF number.
So the greatest common factor 490 and 504 is 14.

Also check out the Least Common Multiple of 490 and 504