What is the Greatest Common Factor of 825 and 840?

Greatest common factor (GCF) of 825 and 840 is 15.

GCF(825,840) = 15

We will now calculate the prime factors of 825 and 840, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 825 and 840.

How to find the GCF of 825 and 840?

We will first find the prime factorization of 825 and 840. After we will calculate the factors of 825 and 840 and find the biggest common factor number .

Step-1: Prime Factorization of 825

Prime factors of 825 are 3, 5, 11. Prime factorization of 825 in exponential form is:

825 = 3¹ × 5² × 11¹

Step-2: Prime Factorization of 840

Prime factors of 840 are 2, 3, 5, 7. Prime factorization of 840 in exponential form is:

840 = 2³ × 3¹ × 5¹ × 7¹

Step-3: Factors of 825

List of positive integer factors of 825 that divides 825 without a remainder.

1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275

Step-4: Factors of 840

List of positive integer factors of 840 that divides 825 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 825 and 840. The biggest common factor number is the GCF number.
So the greatest common factor 825 and 840 is 15.

Also check out the Least Common Multiple of 825 and 840