What is the Greatest Common Factor of 892 and 900?

Greatest common factor (GCF) of 892 and 900 is 4.

GCF(892,900) = 4

We will now calculate the prime factors of 892 and 900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 892 and 900.

How to find the GCF of 892 and 900?

We will first find the prime factorization of 892 and 900. After we will calculate the factors of 892 and 900 and find the biggest common factor number .

Step-1: Prime Factorization of 892

Prime factors of 892 are 2, 223. Prime factorization of 892 in exponential form is:

892 = 2² × 223¹

Step-2: Prime Factorization of 900

Prime factors of 900 are 2, 3, 5. Prime factorization of 900 in exponential form is:

900 = 2² × 3² × 5²

Step-3: Factors of 892

List of positive integer factors of 892 that divides 892 without a remainder.

1, 2, 4, 223, 446

Step-4: Factors of 900

List of positive integer factors of 900 that divides 892 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 892 and 900. The biggest common factor number is the GCF number.
So the greatest common factor 892 and 900 is 4.

Also check out the Least Common Multiple of 892 and 900