What is the Greatest Common Factor of 75762 and 75777?

Greatest common factor (GCF) of 75762 and 75777 is 3.

GCF(75762,75777) = 3

We will now calculate the prime factors of 75762 and 75777, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75762 and 75777.

How to find the GCF of 75762 and 75777?

We will first find the prime factorization of 75762 and 75777. After we will calculate the factors of 75762 and 75777 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75777

Prime factors of 75777 are 3, 13, 29, 67. Prime factorization of 75777 in exponential form is:

75777 = 3¹ × 13¹ × 29¹ × 67¹

Step-3: Factors of 75762

List of positive integer factors of 75762 that divides 75762 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

Step-4: Factors of 75777

List of positive integer factors of 75777 that divides 75762 without a remainder.

1, 3, 13, 29, 39, 67, 87, 201, 377, 871, 1131, 1943, 2613, 5829, 25259

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75762 and 75777. The biggest common factor number is the GCF number.
So the greatest common factor 75762 and 75777 is 3.

Also check out the Least Common Multiple of 75762 and 75777