What is the Greatest Common Factor of 85742 and 85760?

Greatest common factor (GCF) of 85742 and 85760 is 2.

GCF(85742,85760) = 2

We will now calculate the prime factors of 85742 and 85760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85742 and 85760.

How to find the GCF of 85742 and 85760?

We will first find the prime factorization of 85742 and 85760. After we will calculate the factors of 85742 and 85760 and find the biggest common factor number .

Step-1: Prime Factorization of 85742

Prime factors of 85742 are 2, 43, 997. Prime factorization of 85742 in exponential form is:

85742 = 2¹ × 43¹ × 997¹

Step-2: Prime Factorization of 85760

Prime factors of 85760 are 2, 5, 67. Prime factorization of 85760 in exponential form is:

85760 = 2⁸ × 5¹ × 67¹

Step-3: Factors of 85742

List of positive integer factors of 85742 that divides 85742 without a remainder.

1, 2, 43, 86, 997, 1994, 42871

Step-4: Factors of 85760

List of positive integer factors of 85760 that divides 85742 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 67, 80, 128, 134, 160, 256, 268, 320, 335, 536, 640, 670, 1072, 1280, 1340, 2144, 2680, 4288, 5360, 8576, 10720, 17152, 21440, 42880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85742 and 85760. The biggest common factor number is the GCF number.
So the greatest common factor 85742 and 85760 is 2.

Also check out the Least Common Multiple of 85742 and 85760