What is the Greatest Common Factor of 1410 and 1424?

Greatest common factor (GCF) of 1410 and 1424 is 2.

GCF(1410,1424) = 2

We will now calculate the prime factors of 1410 and 1424, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1410 and 1424.

How to find the GCF of 1410 and 1424?

We will first find the prime factorization of 1410 and 1424. After we will calculate the factors of 1410 and 1424 and find the biggest common factor number .

Step-1: Prime Factorization of 1410

Prime factors of 1410 are 2, 3, 5, 47. Prime factorization of 1410 in exponential form is:

1410 = 2¹ × 3¹ × 5¹ × 47¹

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 1410

List of positive integer factors of 1410 that divides 1410 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 47, 94, 141, 235, 282, 470, 705

Step-4: Factors of 1424

List of positive integer factors of 1424 that divides 1410 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 1410 and 1424. The biggest common factor number is the GCF number.
So the greatest common factor 1410 and 1424 is 2.

Also check out the Least Common Multiple of 1410 and 1424