Greatest Common Factor of 10074 and 10080

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 10074, 10080 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 10074 and 10080 is 6.

GCF(10074,10080) = 6

GCF of 10074 and 10080

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 10074 and 10080

GCF of 10074 and 10080 is 6

Prime Factorization of 10074


2 10074
3 5037
23 1679
73 73
1

Prime factors of 10074 are 2,3,23,73. Prime factorization of 10074 in exponential form is:

10074 = 21×31×231×731

Prime Factorization of 10080


2 10080
2 5040
2 2520
2 1260
2 630
3 315
3 105
5 35
7 7
1

Prime factors of 10080 are 2,3,5,7. Prime factorization of 10080 in exponential form is:

10080 = 25×32×51×71

∴ So by taking common prime factors GCF of 10074 and 10080 is 6

Greatest Common Factor of 10074 and 10080 by matching factors method

Factors of 10074

List of positive integer factors of 10074 that divides 10074 without a remainder.

1,2,3,6,23,46,69,73,138,146,219,438,1679,3358,5037,10074

Factors of 10080

List of positive integer factors of 10080 that divides 10080 without a remainder.

1,2,3,4,5,6,7,8,9,10,12,14,15,16,18,20,21,24,28,30,32,35,36,40,42,45,48,56,60,63,70,72,80,84,90,96,105,112,120,126,140,144,160,168,180,210,224,240,252,280,288,315,336,360,420,480,504,560,630,672,720,840,1008,1120,1260,1440,1680,2016,2520,3360,5040,10080

Greatest Common Factor

We found the factors and prime factorization of 10074 and 10080. The biggest common factor number is the GCF number.
So the greatest common factor 10074 and 10080 is 6.

Also check out the Least Common Multiple of 10074 and 10080

Properties of GCF 10074 and 10080

(i) The GCF of 10074 and 10080 is associative

GCF of 10074 and 10080 = GCF of 10080 and 10074

Related Greatest Common Factor of 10074

Related Greatest Common Factor of 10080

Frequently Asked Questions on GCF of 10074 and 10080

1. What is the GCF of 10074 and 10080?

Answer: GCF of 10074 and 10080 is 6.

2. What are the Factors of 10074?

Answer: Factors of 10074 are 1, 2, 3, 6, 23, 46, 69, 73, 138, 146, 219, 438, 1679, 3358, 5037, 10074. There are 16 integers that are factors of 10074. The greatest factor of 10074 is 10074.

3. What are the Factors of 10080?

Answer: Factors of 10080 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 140, 144, 160, 168, 180, 210, 224, 240, 252, 280, 288, 315, 336, 360, 420, 480, 504, 560, 630, 672, 720, 840, 1008, 1120, 1260, 1440, 1680, 2016, 2520, 3360, 5040, 10080. There are 72 integers that are factors of 10080. The greatest factor of 10080 is 10080.

4. How to Find the GCF of 10074 and 10080?

Answer:

Greatest Common Factor of 10074 and 10080 = 6

Step 1: Find the prime factorization of 10074

10074 = 2 x 3 x 23 x 73

Step 2: Find the prime factorization of 10080

10080 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 10074 and 10080 is 6