What is the Greatest Common Factor of 35742 and 35757?

Greatest common factor (GCF) of 35742 and 35757 is 3.

GCF(35742,35757) = 3

We will now calculate the prime factors of 35742 and 35757, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35742 and 35757.

How to find the GCF of 35742 and 35757?

We will first find the prime factorization of 35742 and 35757. After we will calculate the factors of 35742 and 35757 and find the biggest common factor number .

Step-1: Prime Factorization of 35742

Prime factors of 35742 are 2, 3, 7, 23, 37. Prime factorization of 35742 in exponential form is:

35742 = 2¹ × 3¹ × 7¹ × 23¹ × 37¹

Step-2: Prime Factorization of 35757

Prime factors of 35757 are 3, 29, 137. Prime factorization of 35757 in exponential form is:

35757 = 3² × 29¹ × 137¹

Step-3: Factors of 35742

List of positive integer factors of 35742 that divides 35742 without a remainder.

1, 2, 3, 6, 7, 14, 21, 23, 37, 42, 46, 69, 74, 111, 138, 161, 222, 259, 322, 483, 518, 777, 851, 966, 1554, 1702, 2553, 5106, 5957, 11914, 17871

Step-4: Factors of 35757

List of positive integer factors of 35757 that divides 35742 without a remainder.

1, 3, 9, 29, 87, 137, 261, 411, 1233, 3973, 11919

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35742 and 35757. The biggest common factor number is the GCF number.
So the greatest common factor 35742 and 35757 is 3.

Also check out the Least Common Multiple of 35742 and 35757