What is the Greatest Common Factor of 3500 and 3504?

Greatest common factor (GCF) of 3500 and 3504 is 4.

GCF(3500,3504) = 4

We will now calculate the prime factors of 3500 and 3504, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3500 and 3504.

How to find the GCF of 3500 and 3504?

We will first find the prime factorization of 3500 and 3504. After we will calculate the factors of 3500 and 3504 and find the biggest common factor number .

Step-1: Prime Factorization of 3500

Prime factors of 3500 are 2, 5, 7. Prime factorization of 3500 in exponential form is:

3500 = 2² × 5³ × 7¹

Step-2: 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-3: Factors of 3500

List of positive integer factors of 3500 that divides 3500 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 700, 875, 1750

Step-4: Factors of 3504

List of positive integer factors of 3504 that divides 3500 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3500 and 3504. The biggest common factor number is the GCF number.
So the greatest common factor 3500 and 3504 is 4.

Also check out the Least Common Multiple of 3500 and 3504