What is the Greatest Common Factor of 1449 and 1456?

Greatest common factor (GCF) of 1449 and 1456 is 7.

GCF(1449,1456) = 7

We will now calculate the prime factors of 1449 and 1456, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1449 and 1456.

How to find the GCF of 1449 and 1456?

We will first find the prime factorization of 1449 and 1456. After we will calculate the factors of 1449 and 1456 and find the biggest common factor number .

Step-1: Prime Factorization of 1449

Prime factors of 1449 are 3, 7, 23. Prime factorization of 1449 in exponential form is:

1449 = 3² × 7¹ × 23¹

Step-2: Prime Factorization of 1456

Prime factors of 1456 are 2, 7, 13. Prime factorization of 1456 in exponential form is:

1456 = 2⁴ × 7¹ × 13¹

Step-3: Factors of 1449

List of positive integer factors of 1449 that divides 1449 without a remainder.

1, 3, 7, 9, 21, 23, 63, 69, 161, 207, 483

Step-4: Factors of 1456

List of positive integer factors of 1456 that divides 1449 without a remainder.

1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 52, 56, 91, 104, 112, 182, 208, 364, 728

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1449 and 1456. The biggest common factor number is the GCF number.
So the greatest common factor 1449 and 1456 is 7.

Also check out the Least Common Multiple of 1449 and 1456