What is the Greatest Common Factor of 75746 and 75762?

Greatest common factor (GCF) of 75746 and 75762 is 2.

GCF(75746,75762) = 2

We will now calculate the prime factors of 75746 and 75762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75746 and 75762.

How to find the GCF of 75746 and 75762?

We will first find the prime factorization of 75746 and 75762. After we will calculate the factors of 75746 and 75762 and find the biggest common factor number .

Step-1: Prime Factorization of 75746

Prime factors of 75746 are 2, 11, 313. Prime factorization of 75746 in exponential form is:

75746 = 2¹ × 11² × 313¹

Step-2: Prime Factorization of 75762

Prime factors of 75762 are 2, 3, 23, 61. Prime factorization of 75762 in exponential form is:

75762 = 2¹ × 3³ × 23¹ × 61¹

Step-3: Factors of 75746

List of positive integer factors of 75746 that divides 75746 without a remainder.

1, 2, 11, 22, 121, 242, 313, 626, 3443, 6886, 37873

Step-4: Factors of 75762

List of positive integer factors of 75762 that divides 75746 without a remainder.

1, 2, 3, 6, 9, 18, 23, 27, 46, 54, 61, 69, 122, 138, 183, 207, 366, 414, 549, 621, 1098, 1242, 1403, 1647, 2806, 3294, 4209, 8418, 12627, 25254, 37881

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75746 and 75762. The biggest common factor number is the GCF number.
So the greatest common factor 75746 and 75762 is 2.

Also check out the Least Common Multiple of 75746 and 75762