What is the Greatest Common Factor of 5250 and 5264?

Greatest common factor (GCF) of 5250 and 5264 is 14.

GCF(5250,5264) = 14

We will now calculate the prime factors of 5250 and 5264, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5250 and 5264.

How to find the GCF of 5250 and 5264?

We will first find the prime factorization of 5250 and 5264. After we will calculate the factors of 5250 and 5264 and find the biggest common factor number .

Step-1: Prime Factorization of 5250

Prime factors of 5250 are 2, 3, 5, 7. Prime factorization of 5250 in exponential form is:

5250 = 2¹ × 3¹ × 5³ × 7¹

Step-2: Prime Factorization of 5264

Prime factors of 5264 are 2, 7, 47. Prime factorization of 5264 in exponential form is:

5264 = 2⁴ × 7¹ × 47¹

Step-3: Factors of 5250

List of positive integer factors of 5250 that divides 5250 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 125, 150, 175, 210, 250, 350, 375, 525, 750, 875, 1050, 1750, 2625

Step-4: Factors of 5264

List of positive integer factors of 5264 that divides 5250 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 47, 56, 94, 112, 188, 329, 376, 658, 752, 1316, 2632

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5250 and 5264. The biggest common factor number is the GCF number.
So the greatest common factor 5250 and 5264 is 14.

Also check out the Least Common Multiple of 5250 and 5264