What is the Greatest Common Factor of 3504 and 3514?

Greatest common factor (GCF) of 3504 and 3514 is 2.

GCF(3504,3514) = 2

We will now calculate the prime factors of 3504 and 3514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3504 and 3514.

How to find the GCF of 3504 and 3514?

We will first find the prime factorization of 3504 and 3514. After we will calculate the factors of 3504 and 3514 and find the biggest common factor number .

Step-1: Prime Factorization of 3504

Prime factors of 3504 are 2, 3, 73. Prime factorization of 3504 in exponential form is:

3504 = 2⁴ × 3¹ × 73¹

Step-2: Prime Factorization of 3514

Prime factors of 3514 are 2, 7, 251. Prime factorization of 3514 in exponential form is:

3514 = 2¹ × 7¹ × 251¹

Step-3: Factors of 3504

List of positive integer factors of 3504 that divides 3504 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 73, 146, 219, 292, 438, 584, 876, 1168, 1752

Step-4: Factors of 3514

List of positive integer factors of 3514 that divides 3504 without a remainder.

1, 2, 7, 14, 251, 502, 1757

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3504 and 3514. The biggest common factor number is the GCF number.
So the greatest common factor 3504 and 3514 is 2.

Also check out the Least Common Multiple of 3504 and 3514