What is the Greatest Common Factor of 35840 and 35854?

Greatest common factor (GCF) of 35840 and 35854 is 14.

GCF(35840,35854) = 14

We will now calculate the prime factors of 35840 and 35854, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35840 and 35854.

How to find the GCF of 35840 and 35854?

We will first find the prime factorization of 35840 and 35854. After we will calculate the factors of 35840 and 35854 and find the biggest common factor number .

Step-1: Prime Factorization of 35840

Prime factors of 35840 are 2, 5, 7. Prime factorization of 35840 in exponential form is:

35840 = 2¹⁰ × 5¹ × 7¹

Step-2: Prime Factorization of 35854

Prime factors of 35854 are 2, 7, 13, 197. Prime factorization of 35854 in exponential form is:

35854 = 2¹ × 7¹ × 13¹ × 197¹

Step-3: Factors of 35840

List of positive integer factors of 35840 that divides 35840 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 64, 70, 80, 112, 128, 140, 160, 224, 256, 280, 320, 448, 512, 560, 640, 896, 1024, 1120, 1280, 1792, 2240, 2560, 3584, 4480, 5120, 7168, 8960, 17920

Step-4: Factors of 35854

List of positive integer factors of 35854 that divides 35840 without a remainder.

1, 2, 7, 13, 14, 26, 91, 182, 197, 394, 1379, 2561, 2758, 5122, 17927

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35840 and 35854. The biggest common factor number is the GCF number.
So the greatest common factor 35840 and 35854 is 14.

Also check out the Least Common Multiple of 35840 and 35854