What is the Greatest Common Factor of 5235 and 5250?

Greatest common factor (GCF) of 5235 and 5250 is 15.

GCF(5235,5250) = 15

We will now calculate the prime factors of 5235 and 5250, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5235 and 5250.

How to find the GCF of 5235 and 5250?

We will first find the prime factorization of 5235 and 5250. After we will calculate the factors of 5235 and 5250 and find the biggest common factor number .

Step-1: Prime Factorization of 5235

Prime factors of 5235 are 3, 5, 349. Prime factorization of 5235 in exponential form is:

5235 = 3¹ × 5¹ × 349¹

Step-2: 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-3: Factors of 5235

List of positive integer factors of 5235 that divides 5235 without a remainder.

1, 3, 5, 15, 349, 1047, 1745

Step-4: Factors of 5250

List of positive integer factors of 5250 that divides 5235 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5235 and 5250. The biggest common factor number is the GCF number.
So the greatest common factor 5235 and 5250 is 15.

Also check out the Least Common Multiple of 5235 and 5250