What is the Greatest Common Factor of 1402 and 1408?

Greatest common factor (GCF) of 1402 and 1408 is 2.

GCF(1402,1408) = 2

We will now calculate the prime factors of 1402 and 1408, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1402 and 1408.

How to find the GCF of 1402 and 1408?

We will first find the prime factorization of 1402 and 1408. After we will calculate the factors of 1402 and 1408 and find the biggest common factor number .

Step-1: Prime Factorization of 1402

Prime factors of 1402 are 2, 701. Prime factorization of 1402 in exponential form is:

1402 = 2¹ × 701¹

Step-2: Prime Factorization of 1408

Prime factors of 1408 are 2, 11. Prime factorization of 1408 in exponential form is:

1408 = 2⁷ × 11¹

Step-3: Factors of 1402

List of positive integer factors of 1402 that divides 1402 without a remainder.

1, 2, 701

Step-4: Factors of 1408

List of positive integer factors of 1408 that divides 1402 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 128, 176, 352, 704

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1402 and 1408. The biggest common factor number is the GCF number.
So the greatest common factor 1402 and 1408 is 2.

Also check out the Least Common Multiple of 1402 and 1408