What is the Greatest Common Factor of 1040 and 1054?

Greatest common factor (GCF) of 1040 and 1054 is 2.

GCF(1040,1054) = 2

We will now calculate the prime factors of 1040 and 1054, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1040 and 1054.

How to find the GCF of 1040 and 1054?

We will first find the prime factorization of 1040 and 1054. After we will calculate the factors of 1040 and 1054 and find the biggest common factor number .

Step-1: Prime Factorization of 1040

Prime factors of 1040 are 2, 5, 13. Prime factorization of 1040 in exponential form is:

1040 = 2⁴ × 5¹ × 13¹

Step-2: Prime Factorization of 1054

Prime factors of 1054 are 2, 17, 31. Prime factorization of 1054 in exponential form is:

1054 = 2¹ × 17¹ × 31¹

Step-3: Factors of 1040

List of positive integer factors of 1040 that divides 1040 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 40, 52, 65, 80, 104, 130, 208, 260, 520

Step-4: Factors of 1054

List of positive integer factors of 1054 that divides 1040 without a remainder.

1, 2, 17, 31, 34, 62, 527

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1040 and 1054. The biggest common factor number is the GCF number.
So the greatest common factor 1040 and 1054 is 2.

Also check out the Least Common Multiple of 1040 and 1054