What is the Greatest Common Factor of 1402 and 1410?

Greatest common factor (GCF) of 1402 and 1410 is 2.

GCF(1402,1410) = 2

We will now calculate the prime factors of 1402 and 1410, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1402 and 1410.

How to find the GCF of 1402 and 1410?

We will first find the prime factorization of 1402 and 1410. After we will calculate the factors of 1402 and 1410 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 1410

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

1410 = 2¹ × 3¹ × 5¹ × 47¹

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 1410

List of positive integer factors of 1410 that divides 1402 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1402 and 1410. The biggest common factor number is the GCF number.
So the greatest common factor 1402 and 1410 is 2.

Also check out the Least Common Multiple of 1402 and 1410