How to Find GCF of 678/47, 780/582?

GCF of 678/47, 780/582

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 678/47, 780/582 i.e 6/27354 easily. The following is the detailed procedure to determine the greatest common factor of fractions 678/47, 780/582.

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 678/47,780/582?

Given fractions are 678/47,780/582

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 678/47,780/582, numerators are 678,780

Denominators are 47,582

The GCF of 678,780 is 6 .

LCM of 47,582 is 27354.

The greatest common factor of 678/47,780/582 = [GCF of 678,780]/[LCM of 47,582]= 6/27354

Therefore, the GCF of 678/47,780/582 is 6/27354.

Greatest Common Factor of 678,780

To find the highest common factor of 678,780, we have to find the factors of both numbers and list the highest common factor.

The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678

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 HCF of 678,780 is 6.

Lets's calculate GCF of 678,780

Greatest Common Factor (GCF) of 678,780 By Common Division

2	678, 780
3	339, 390
	113, 130

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 678,780 By Matching Biggest Common Factor Method

Now, list down the factors of 678

1,2,3,6,113,226,339,678

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

Greatest Common Factor

We found the factors 678,780 . The biggest common factor number is the GCF number.
So the greatest common factor 678,780 is 6.

Lets's calculate LCM of 47,582

Lowest Common Multiple of 47,582 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 27354

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/27354

Therefore, the GCF of Fractions 678/47,780/582 is 6/27354

Least Common Multiple of 47,582 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 47,582 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(47,582) = 1

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

GCF(47,582) x common factors =1 x 1 = 1

LCM(47,582) = ( 47 × 582 ) / 1

LCM(47,582) = 27354 / 1

LCM(47,582) = 27354

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FAQs on GCF of Fractions of 678/47, 780/582

1. What is the HCF of 678,780?

The HCF of 678,780 is 6

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 678/47, 780/582?

Answer: GCF of Numerators as per given numbers 678/47, 780/582 is

GCF of Numerators i.e. for 678,780 is 6

LCM of denominators i.e. for 47,582 is 27354.

Thus, GCF of Fractions is 6/27354.Finally, GCF of Fractions for 678/47, 780/582 is 6/27354.