What is the Greatest Common Factor of 1412 and 1428?

Greatest common factor (GCF) of 1412 and 1428 is 4.

GCF(1412,1428) = 4

We will now calculate the prime factors of 1412 and 1428, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1412 and 1428.

How to find the GCF of 1412 and 1428?

We will first find the prime factorization of 1412 and 1428. After we will calculate the factors of 1412 and 1428 and find the biggest common factor number .

Step-1: Prime Factorization of 1412

Prime factors of 1412 are 2, 353. Prime factorization of 1412 in exponential form is:

1412 = 2² × 353¹

Step-2: Prime Factorization of 1428

Prime factors of 1428 are 2, 3, 7, 17. Prime factorization of 1428 in exponential form is:

1428 = 2² × 3¹ × 7¹ × 17¹

Step-3: Factors of 1412

List of positive integer factors of 1412 that divides 1412 without a remainder.

1, 2, 4, 353, 706

Step-4: Factors of 1428

List of positive integer factors of 1428 that divides 1412 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 51, 68, 84, 102, 119, 204, 238, 357, 476, 714

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1412 and 1428. The biggest common factor number is the GCF number.
So the greatest common factor 1412 and 1428 is 4.

Also check out the Least Common Multiple of 1412 and 1428