How to Find GCF of 780/408, 454/374?

GCF of 780/408, 454/374

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 780/408, 454/374 i.e 2/4488 easily. The following is the detailed procedure to determine the greatest common factor of fractions 780/408, 454/374.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 780/408,454/374?

Given fractions are 780/408,454/374

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 780/408,454/374, numerators are 780,454

Denominators are 408,374

The GCF of 780,454 is 2 .

LCM of 408,374 is 4488.

The greatest common factor of 780/408,454/374 = [GCF of 780,454]/[LCM of 408,374]= 2/4488

Therefore, the GCF of 780/408,454/374 is 2/4488.

Greatest Common Factor of 780,454

To find the highest common factor of 780,454, we have to find the factors of both numbers and list the highest common factor.

The factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780

The factors of 454 are 1, 2, 227, 454

The HCF of 780,454 is 2.

Lets's calculate GCF of 780,454

Greatest Common Factor (GCF) of 780,454 By Common Division

2	780, 454
	390, 227

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 780,454 By Matching Biggest Common Factor Method

Now, list down the factors of 780

1,2,3,4,5,6,10,12,13,15,20,26,30,39,52,60,65,78,130,156,195,260,390,780

Now, list down the factors of 454

1,2,227,454

Greatest Common Factor

We found the factors 780,454 . The biggest common factor number is the GCF number.
So the greatest common factor 780,454 is 2.

Lets's calculate LCM of 408,374

Lowest Common Multiple of 408,374 using Common Division

2	408, 374
17	204, 187
	12, 11

∴ So the LCM of the given numbers is 2 x 17 x 12 x 11 = 4488

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/4488

Therefore, the GCF of Fractions 780/408,454/374 is 2/4488

Least Common Multiple of 408,374 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 408,374 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(408,374) = 34

common factors(in case of two or more numbers have common factors) = 1

GCF(408,374) x common factors =34 x 1 = 34

LCM(408,374) = ( 408 × 374 ) / 34

LCM(408,374) = 152592 / 34

LCM(408,374) = 4488

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 780/408, 454/374

1. What is the HCF of 780,454?

The HCF of 780,454 is 2

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 780/408, 454/374?

Answer: GCF of Numerators as per given numbers 780/408, 454/374 is

GCF of Numerators i.e. for 780,454 is 2

LCM of denominators i.e. for 408,374 is 4488.

Thus, GCF of Fractions is 2/4488.Finally, GCF of Fractions for 780/408, 454/374 is 2/4488.