What is the Greatest Common Factor of 1004 and 1010?

Greatest common factor (GCF) of 1004 and 1010 is 2.

GCF(1004,1010) = 2

We will now calculate the prime factors of 1004 and 1010, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1004 and 1010.

How to find the GCF of 1004 and 1010?

We will first find the prime factorization of 1004 and 1010. After we will calculate the factors of 1004 and 1010 and find the biggest common factor number .

Step-1: Prime Factorization of 1004

Prime factors of 1004 are 2, 251. Prime factorization of 1004 in exponential form is:

1004 = 2² × 251¹

Step-2: Prime Factorization of 1010

Prime factors of 1010 are 2, 5, 101. Prime factorization of 1010 in exponential form is:

1010 = 2¹ × 5¹ × 101¹

Step-3: Factors of 1004

List of positive integer factors of 1004 that divides 1004 without a remainder.

1, 2, 4, 251, 502

Step-4: Factors of 1010

List of positive integer factors of 1010 that divides 1004 without a remainder.

1, 2, 5, 10, 101, 202, 505

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1004 and 1010. The biggest common factor number is the GCF number.
So the greatest common factor 1004 and 1010 is 2.

Also check out the Least Common Multiple of 1004 and 1010