What is the Greatest Common Factor of 5250 and 5270?

Greatest common factor (GCF) of 5250 and 5270 is 10.

GCF(5250,5270) = 10

We will now calculate the prime factors of 5250 and 5270, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5250 and 5270.

How to find the GCF of 5250 and 5270?

We will first find the prime factorization of 5250 and 5270. After we will calculate the factors of 5250 and 5270 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 5270

Prime factors of 5270 are 2, 5, 17, 31. Prime factorization of 5270 in exponential form is:

5270 = 2¹ × 5¹ × 17¹ × 31¹

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 5270

List of positive integer factors of 5270 that divides 5250 without a remainder.

1, 2, 5, 10, 17, 31, 34, 62, 85, 155, 170, 310, 527, 1054, 2635

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5250 and 5270. The biggest common factor number is the GCF number.
So the greatest common factor 5250 and 5270 is 10.

Also check out the Least Common Multiple of 5250 and 5270