What is the Greatest Common Factor of 1406 and 1424?

Greatest common factor (GCF) of 1406 and 1424 is 2.

GCF(1406,1424) = 2

We will now calculate the prime factors of 1406 and 1424, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1406 and 1424.

How to find the GCF of 1406 and 1424?

We will first find the prime factorization of 1406 and 1424. After we will calculate the factors of 1406 and 1424 and find the biggest common factor number .

Step-1: Prime Factorization of 1406

Prime factors of 1406 are 2, 19, 37. Prime factorization of 1406 in exponential form is:

1406 = 2¹ × 19¹ × 37¹

Step-2: Prime Factorization of 1424

Prime factors of 1424 are 2, 89. Prime factorization of 1424 in exponential form is:

1424 = 2⁴ × 89¹

Step-3: Factors of 1406

List of positive integer factors of 1406 that divides 1406 without a remainder.

1, 2, 19, 37, 38, 74, 703

Step-4: Factors of 1424

List of positive integer factors of 1424 that divides 1406 without a remainder.

1, 2, 4, 8, 16, 89, 178, 356, 712

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1406 and 1424. The biggest common factor number is the GCF number.
So the greatest common factor 1406 and 1424 is 2.

Also check out the Least Common Multiple of 1406 and 1424