What is the Greatest Common Factor of 32742 and 32760?

Greatest common factor (GCF) of 32742 and 32760 is 18.

GCF(32742,32760) = 18

We will now calculate the prime factors of 32742 and 32760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32742 and 32760.

How to find the GCF of 32742 and 32760?

We will first find the prime factorization of 32742 and 32760. After we will calculate the factors of 32742 and 32760 and find the biggest common factor number .

Step-1: Prime Factorization of 32742

Prime factors of 32742 are 2, 3, 17, 107. Prime factorization of 32742 in exponential form is:

32742 = 2¹ × 3² × 17¹ × 107¹

Step-2: Prime Factorization of 32760

Prime factors of 32760 are 2, 3, 5, 7, 13. Prime factorization of 32760 in exponential form is:

32760 = 2³ × 3² × 5¹ × 7¹ × 13¹

Step-3: Factors of 32742

List of positive integer factors of 32742 that divides 32742 without a remainder.

1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 107, 153, 214, 306, 321, 642, 963, 1819, 1926, 3638, 5457, 10914, 16371

Step-4: Factors of 32760

List of positive integer factors of 32760 that divides 32742 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 18, 20, 21, 24, 26, 28, 30, 35, 36, 39, 40, 42, 45, 52, 56, 60, 63, 65, 70, 72, 78, 84, 90, 91, 104, 105, 117, 120, 126, 130, 140, 156, 168, 180, 182, 195, 210, 234, 252, 260, 273, 280, 312, 315, 360, 364, 390, 420, 455, 468, 504, 520, 546, 585, 630, 728, 780, 819, 840, 910, 936, 1092, 1170, 1260, 1365, 1560, 1638, 1820, 2184, 2340, 2520, 2730, 3276, 3640, 4095, 4680, 5460, 6552, 8190, 10920, 16380

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32742 and 32760. The biggest common factor number is the GCF number.
So the greatest common factor 32742 and 32760 is 18.

Also check out the Least Common Multiple of 32742 and 32760