What is the Greatest Common Factor of 61536 and 61542?

Greatest common factor (GCF) of 61536 and 61542 is 6.

GCF(61536,61542) = 6

We will now calculate the prime factors of 61536 and 61542, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61536 and 61542.

How to find the GCF of 61536 and 61542?

We will first find the prime factorization of 61536 and 61542. After we will calculate the factors of 61536 and 61542 and find the biggest common factor number .

Step-1: Prime Factorization of 61536

Prime factors of 61536 are 2, 3, 641. Prime factorization of 61536 in exponential form is:

61536 = 2⁵ × 3¹ × 641¹

Step-2: Prime Factorization of 61542

Prime factors of 61542 are 2, 3, 13, 263. Prime factorization of 61542 in exponential form is:

61542 = 2¹ × 3² × 13¹ × 263¹

Step-3: Factors of 61536

List of positive integer factors of 61536 that divides 61536 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 641, 1282, 1923, 2564, 3846, 5128, 7692, 10256, 15384, 20512, 30768

Step-4: Factors of 61542

List of positive integer factors of 61542 that divides 61536 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234, 263, 526, 789, 1578, 2367, 3419, 4734, 6838, 10257, 20514, 30771

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61536 and 61542. The biggest common factor number is the GCF number.
So the greatest common factor 61536 and 61542 is 6.

Also check out the Least Common Multiple of 61536 and 61542