What is the Greatest Common Factor of 1428 and 1448?

Greatest common factor (GCF) of 1428 and 1448 is 4.

GCF(1428,1448) = 4

We will now calculate the prime factors of 1428 and 1448, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1428 and 1448.

How to find the GCF of 1428 and 1448?

We will first find the prime factorization of 1428 and 1448. After we will calculate the factors of 1428 and 1448 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 1448

Prime factors of 1448 are 2, 181. Prime factorization of 1448 in exponential form is:

1448 = 2³ × 181¹

Step-3: Factors of 1428

List of positive integer factors of 1428 that divides 1428 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

Step-4: Factors of 1448

List of positive integer factors of 1448 that divides 1428 without a remainder.

1, 2, 4, 8, 181, 362, 724

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1428 and 1448. The biggest common factor number is the GCF number.
So the greatest common factor 1428 and 1448 is 4.

Also check out the Least Common Multiple of 1428 and 1448