What is the Greatest Common Factor of 480 and 490?

Greatest common factor (GCF) of 480 and 490 is 10.

GCF(480,490) = 10

We will now calculate the prime factors of 480 and 490, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 480 and 490.

How to find the GCF of 480 and 490?

We will first find the prime factorization of 480 and 490. After we will calculate the factors of 480 and 490 and find the biggest common factor number .

Step-1: Prime Factorization of 480

Prime factors of 480 are 2, 3, 5. Prime factorization of 480 in exponential form is:

480 = 2⁵ × 3¹ × 5¹

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 480

List of positive integer factors of 480 that divides 480 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240

Step-4: Factors of 490

List of positive integer factors of 490 that divides 480 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 480 and 490. The biggest common factor number is the GCF number.
So the greatest common factor 480 and 490 is 10.

Also check out the Least Common Multiple of 480 and 490