How to Find GCF of 51/59, 653/64, 114/828?

GCF of 51/59, 653/64, 114/828

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 51/59, 653/64, 114/828 i.e 1/781632 easily. The following is the detailed procedure to determine the greatest common factor of fractions 51/59, 653/64, 114/828.

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 51/59,653/64,114/828?

Given fractions are 51/59,653/64,114/828

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 51/59,653/64,114/828, numerators are 51,653,114

Denominators are 59,64,828

The GCF of 51,653,114 is 1 .

LCM of 59,64,828 is 781632.

The greatest common factor of 51/59,653/64,114/828 = [GCF of 51,653,114]/[LCM of 59,64,828]= 1/781632

Therefore, the GCF of 51/59,653/64,114/828 is 1/781632.

Greatest Common Factor of 51,653,114

To find the highest common factor of 51,653,114, we have to find the factors of both numbers and list the highest common factor.

The factors of 51 are 1, 3, 17, 51

The factors of 653 are 1, 653

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

The HCF of 51,653,114 is 1.

Lets's calculate GCF of 51,653,114

Greatest Common Factor (GCF) of 51,653,114 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 51,653,114 By Matching Biggest Common Factor Method

Now, list down the factors of 51

1,3,17,51

Now, list down the factors of 653

1,653

Now, list down the factors of 114

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

Greatest Common Factor

We found the factors 51,653,114 . The biggest common factor number is the GCF number.
So the greatest common factor 51,653,114 is 1.

Lets's calculate LCM of 59,64,828

Lowest Common Multiple of 59,64,828 using Common Division

2	59, 64, 828
2	59, 32, 414
	59, 16, 207

∴ So the LCM of the given numbers is 2 x 2 x 59 x 16 x 207 = 781632

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/781632

Therefore, the GCF of Fractions 51/59,653/64,114/828 is 1/781632

Least Common Multiple of 59,64,828 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 59,64,828 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(59,64,828) = 1

common factors(in case of two or more numbers have common factors) = 4

GCF(59,64,828) x common factors =1 x 4 = 4

LCM(59,64,828) = ( 59 × 64 × 828 ) / 4

LCM(59,64,828) = 3126528 / 4

LCM(59,64,828) = 781632

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 51/59, 653/64, 114/828

1. What is the HCF of 51,653,114?

The HCF of 51,653,114 is 1

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 51/59, 653/64, 114/828?

Answer: GCF of Numerators as per given numbers 51/59, 653/64, 114/828 is

GCF of Numerators i.e. for 51,653,114 is 1

LCM of denominators i.e. for 59,64,828 is 781632.

Thus, GCF of Fractions is 1/781632.Finally, GCF of Fractions for 51/59, 653/64, 114/828 is 1/781632.