What is the Greatest Common Factor of 10738 and 10752?

Greatest common factor (GCF) of 10738 and 10752 is 14.

GCF(10738,10752) = 14

We will now calculate the prime factors of 10738 and 10752, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10738 and 10752.

How to find the GCF of 10738 and 10752?

We will first find the prime factorization of 10738 and 10752. After we will calculate the factors of 10738 and 10752 and find the biggest common factor number .

Step-1: Prime Factorization of 10738

Prime factors of 10738 are 2, 7, 13, 59. Prime factorization of 10738 in exponential form is:

10738 = 2¹ × 7¹ × 13¹ × 59¹

Step-2: Prime Factorization of 10752

Prime factors of 10752 are 2, 3, 7. Prime factorization of 10752 in exponential form is:

10752 = 2⁹ × 3¹ × 7¹

Step-3: Factors of 10738

List of positive integer factors of 10738 that divides 10738 without a remainder.

1, 2, 7, 13, 14, 26, 59, 91, 118, 182, 413, 767, 826, 1534, 5369

Step-4: Factors of 10752

List of positive integer factors of 10752 that divides 10738 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 64, 84, 96, 112, 128, 168, 192, 224, 256, 336, 384, 448, 512, 672, 768, 896, 1344, 1536, 1792, 2688, 3584, 5376

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10738 and 10752. The biggest common factor number is the GCF number.
So the greatest common factor 10738 and 10752 is 14.

Also check out the Least Common Multiple of 10738 and 10752