What is the Greatest Common Factor of 45738 and 45752?

Greatest common factor (GCF) of 45738 and 45752 is 14.

GCF(45738,45752) = 14

We will now calculate the prime factors of 45738 and 45752, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45738 and 45752.

How to find the GCF of 45738 and 45752?

We will first find the prime factorization of 45738 and 45752. After we will calculate the factors of 45738 and 45752 and find the biggest common factor number .

Step-1: Prime Factorization of 45738

Prime factors of 45738 are 2, 3, 7, 11. Prime factorization of 45738 in exponential form is:

45738 = 2¹ × 3³ × 7¹ × 11²

Step-2: Prime Factorization of 45752

Prime factors of 45752 are 2, 7, 19, 43. Prime factorization of 45752 in exponential form is:

45752 = 2³ × 7¹ × 19¹ × 43¹

Step-3: Factors of 45738

List of positive integer factors of 45738 that divides 45738 without a remainder.

1, 2, 3, 6, 7, 9, 11, 14, 18, 21, 22, 27, 33, 42, 54, 63, 66, 77, 99, 121, 126, 154, 189, 198, 231, 242, 297, 363, 378, 462, 594, 693, 726, 847, 1089, 1386, 1694, 2079, 2178, 2541, 3267, 4158, 5082, 6534, 7623, 15246, 22869

Step-4: Factors of 45752

List of positive integer factors of 45752 that divides 45738 without a remainder.

1, 2, 4, 7, 8, 14, 19, 28, 38, 43, 56, 76, 86, 133, 152, 172, 266, 301, 344, 532, 602, 817, 1064, 1204, 1634, 2408, 3268, 5719, 6536, 11438, 22876

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45738 and 45752. The biggest common factor number is the GCF number.
So the greatest common factor 45738 and 45752 is 14.

Also check out the Least Common Multiple of 45738 and 45752