Greatest Common Factor of 1440 and 1448

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 1440, 1448 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1440 and 1448 is 8.

GCF(1440,1448) = 8

GCF of 1440 and 1448

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

GCF of:
and

Greatest Common Factor of 1440 and 1448

GCF of 1440 and 1448 is 8

Prime Factorization of 1440


2 1440
2 720
2 360
2 180
2 90
3 45
3 15
5 5
1

Prime factors of 1440 are 2,3,5. Prime factorization of 1440 in exponential form is:

1440 = 25×32×51

Prime Factorization of 1448


2 1448
2 724
2 362
181 181
1

Prime factors of 1448 are 2,181. Prime factorization of 1448 in exponential form is:

1448 = 23×1811

∴ So by taking common prime factors GCF of 1440 and 1448 is 8

Greatest Common Factor of 1440 and 1448 by matching factors method

Factors of 1440

List of positive integer factors of 1440 that divides 1440 without a remainder.

1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,30,32,36,40,45,48,60,72,80,90,96,120,144,160,180,240,288,360,480,720,1440

Factors of 1448

List of positive integer factors of 1448 that divides 1448 without a remainder.

1,2,4,8,181,362,724,1448

Greatest Common Factor

We found the factors and prime factorization of 1440 and 1448. The biggest common factor number is the GCF number.
So the greatest common factor 1440 and 1448 is 8.

Also check out the Least Common Multiple of 1440 and 1448

Properties of GCF 1440 and 1448

(i) The GCF of 1440 and 1448 is associative

GCF of 1440 and 1448 = GCF of 1448 and 1440

Related Greatest Common Factor of 1440

Related Greatest Common Factor of 1448

Frequently Asked Questions on GCF of 1440 and 1448

1. What is the GCF of 1440 and 1448?

Answer: GCF of 1440 and 1448 is 8.

2. What are the Factors of 1440?

Answer: Factors of 1440 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 72, 80, 90, 96, 120, 144, 160, 180, 240, 288, 360, 480, 720, 1440. There are 36 integers that are factors of 1440. The greatest factor of 1440 is 1440.

3. What are the Factors of 1448?

Answer: Factors of 1448 are 1, 2, 4, 8, 181, 362, 724, 1448. There are 8 integers that are factors of 1448. The greatest factor of 1448 is 1448.

4. How to Find the GCF of 1440 and 1448?

Answer:

Greatest Common Factor of 1440 and 1448 = 8

Step 1: Find the prime factorization of 1440

1440 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5

Step 2: Find the prime factorization of 1448

1448 = 2 x 2 x 2 x 181

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

GCF = 2 x 2 x 2 = 8

Step 4: Therefore, the greatest common factor of 1440 and 1448 is 8