What is the Greatest Common Factor of 13650 and 13670?

Greatest common factor (GCF) of 13650 and 13670 is 10.

GCF(13650,13670) = 10

We will now calculate the prime factors of 13650 and 13670, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13650 and 13670.

How to find the GCF of 13650 and 13670?

We will first find the prime factorization of 13650 and 13670. After we will calculate the factors of 13650 and 13670 and find the biggest common factor number .

Step-1: Prime Factorization of 13650

Prime factors of 13650 are 2, 3, 5, 7, 13. Prime factorization of 13650 in exponential form is:

13650 = 2¹ × 3¹ × 5² × 7¹ × 13¹

Step-2: Prime Factorization of 13670

Prime factors of 13670 are 2, 5, 1367. Prime factorization of 13670 in exponential form is:

13670 = 2¹ × 5¹ × 1367¹

Step-3: Factors of 13650

List of positive integer factors of 13650 that divides 13650 without a remainder.

1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 21, 25, 26, 30, 35, 39, 42, 50, 65, 70, 75, 78, 91, 105, 130, 150, 175, 182, 195, 210, 273, 325, 350, 390, 455, 525, 546, 650, 910, 975, 1050, 1365, 1950, 2275, 2730, 4550, 6825

Step-4: Factors of 13670

List of positive integer factors of 13670 that divides 13650 without a remainder.

1, 2, 5, 10, 1367, 2734, 6835

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13650 and 13670. The biggest common factor number is the GCF number.
So the greatest common factor 13650 and 13670 is 10.

Also check out the Least Common Multiple of 13650 and 13670