What is the Greatest Common Factor of 3490 and 3510?

Greatest common factor (GCF) of 3490 and 3510 is 10.

GCF(3490,3510) = 10

We will now calculate the prime factors of 3490 and 3510, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3490 and 3510.

How to find the GCF of 3490 and 3510?

We will first find the prime factorization of 3490 and 3510. After we will calculate the factors of 3490 and 3510 and find the biggest common factor number .

Step-1: Prime Factorization of 3490

Prime factors of 3490 are 2, 5, 349. Prime factorization of 3490 in exponential form is:

3490 = 2¹ × 5¹ × 349¹

Step-2: Prime Factorization of 3510

Prime factors of 3510 are 2, 3, 5, 13. Prime factorization of 3510 in exponential form is:

3510 = 2¹ × 3³ × 5¹ × 13¹

Step-3: Factors of 3490

List of positive integer factors of 3490 that divides 3490 without a remainder.

1, 2, 5, 10, 349, 698, 1745

Step-4: Factors of 3510

List of positive integer factors of 3510 that divides 3490 without a remainder.

1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 26, 27, 30, 39, 45, 54, 65, 78, 90, 117, 130, 135, 195, 234, 270, 351, 390, 585, 702, 1170, 1755

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3490 and 3510. The biggest common factor number is the GCF number.
So the greatest common factor 3490 and 3510 is 10.

Also check out the Least Common Multiple of 3490 and 3510