What is the Greatest Common Factor of 6825 and 6840?

Greatest common factor (GCF) of 6825 and 6840 is 15.

GCF(6825,6840) = 15

We will now calculate the prime factors of 6825 and 6840, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6825 and 6840.

How to find the GCF of 6825 and 6840?

We will first find the prime factorization of 6825 and 6840. After we will calculate the factors of 6825 and 6840 and find the biggest common factor number .

Step-1: Prime Factorization of 6825

Prime factors of 6825 are 3, 5, 7, 13. Prime factorization of 6825 in exponential form is:

6825 = 3¹ × 5² × 7¹ × 13¹

Step-2: Prime Factorization of 6840

Prime factors of 6840 are 2, 3, 5, 19. Prime factorization of 6840 in exponential form is:

6840 = 2³ × 3² × 5¹ × 19¹

Step-3: Factors of 6825

List of positive integer factors of 6825 that divides 6825 without a remainder.

1, 3, 5, 7, 13, 15, 21, 25, 35, 39, 65, 75, 91, 105, 175, 195, 273, 325, 455, 525, 975, 1365, 2275

Step-4: Factors of 6840

List of positive integer factors of 6840 that divides 6825 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 19, 20, 24, 30, 36, 38, 40, 45, 57, 60, 72, 76, 90, 95, 114, 120, 152, 171, 180, 190, 228, 285, 342, 360, 380, 456, 570, 684, 760, 855, 1140, 1368, 1710, 2280, 3420

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6825 and 6840. The biggest common factor number is the GCF number.
So the greatest common factor 6825 and 6840 is 15.

Also check out the Least Common Multiple of 6825 and 6840