What is the Greatest Common Factor of 490 and 505?

Greatest common factor (GCF) of 490 and 505 is 5.

GCF(490,505) = 5

We will now calculate the prime factors of 490 and 505, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 490 and 505.

How to find the GCF of 490 and 505?

We will first find the prime factorization of 490 and 505. After we will calculate the factors of 490 and 505 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 505

Prime factors of 505 are 5, 101. Prime factorization of 505 in exponential form is:

505 = 5¹ × 101¹

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 505

List of positive integer factors of 505 that divides 490 without a remainder.

1, 5, 101

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 490 and 505. The biggest common factor number is the GCF number.
So the greatest common factor 490 and 505 is 5.

Also check out the Least Common Multiple of 490 and 505