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GCF of 114/77, 665/824

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 114/77, 665/824 i.e 19/63448 easily. The following is the detailed procedure to determine the greatest common factor of fractions 114/77, 665/824.

Enter two or more fractions separated by "commas"

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

GCF of:

What is the GCF of 114/77,665/824?

Given fractions are 114/77,665/824

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 114/77,665/824, numerators are 114,665

Denominators are 77,824

The GCF of 114,665 is 19 .

LCM of 77,824 is 63448.

The greatest common factor of 114/77,665/824 = [GCF of 114,665]/[LCM of 77,824]= 19/63448

Therefore, the GCF of 114/77,665/824 is 19/63448.

Greatest Common Factor of 114,665

To find the highest common factor of 114,665, we have to find the factors of both numbers and list the highest common factor.

The factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114

The factors of 665 are 1, 5, 7, 19, 35, 95, 133, 665

The HCF of 114,665 is 19.

Lets's calculate GCF of 114,665

Greatest Common Factor (GCF) of 114,665 By Common Division

19 114, 665
6, 35

∴ So the GCF of the given numbers is 19 = 19

Greatest Common Factor of 114,665 By Matching Biggest Common Factor Method

Greatest Common Factor of 114,665 By Matching Biggest Common Factor Method

Now, list down the factors of 114

:

1,2,3,6,19,38,57,114

Now, list down the factors of 665

:

1,5,7,19,35,95,133,665

Greatest Common Factor

We found the factors 114,665 . The biggest common factor number is the GCF number.
So the greatest common factor 114,665 is 19.

Lets's calculate LCM of 77,824

Lowest Common Multiple of 77,824 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 63448

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 19/63448

Therefore, the GCF of Fractions 114/77,665/824 is 19/63448

Least Common Multiple of 77,824 with GCF Formula

Least Common Multiple of 77,824 with GCF Formula

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

We need to calculate greatest common factor of 77,824 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(77,824) = 1

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

GCF(77,824) x common factors =1 x 1 = 1

LCM(77,824) = ( 77 × 824 ) / 1

LCM(77,824) = 63448 / 1

LCM(77,824) = 63448


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FAQs on GCF of Fractions of 114/77, 665/824

1. What is the HCF of 114,665?

The HCF of 114,665 is 19

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 114/77, 665/824?

Answer: GCF of Numerators as per given numbers 114/77, 665/824 is

GCF of Numerators i.e. for 114,665 is 19

LCM of denominators i.e. for 77,824 is 63448.

Thus, GCF of Fractions is 19/63448.Finally, GCF of Fractions for 114/77, 665/824 is 19/63448.