How to Find GCF of 68/22, 31/34, 680/495?

GCF of 68/22, 31/34, 680/495

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 68/22, 31/34, 680/495 i.e 1/16830 easily. The following is the detailed procedure to determine the greatest common factor of fractions 68/22, 31/34, 680/495.

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 68/22,31/34,680/495?

Given fractions are 68/22,31/34,680/495

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 68/22,31/34,680/495, numerators are 68,31,680

Denominators are 22,34,495

The GCF of 68,31,680 is 1 .

LCM of 22,34,495 is 16830.

The greatest common factor of 68/22,31/34,680/495 = [GCF of 68,31,680]/[LCM of 22,34,495]= 1/16830

Therefore, the GCF of 68/22,31/34,680/495 is 1/16830.

Greatest Common Factor of 68,31,680

To find the highest common factor of 68,31,680, we have to find the factors of both numbers and list the highest common factor.

The factors of 68 are 1, 2, 4, 17, 34, 68

The factors of 31 are 1, 31

The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680

The HCF of 68,31,680 is 1.

Lets's calculate GCF of 68,31,680

Greatest Common Factor (GCF) of 68,31,680 By Common Division

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

Greatest Common Factor of 68,31,680 By Matching Biggest Common Factor Method

Now, list down the factors of 68

1,2,4,17,34,68

Now, list down the factors of 31

1,31

Now, list down the factors of 680

1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680

Greatest Common Factor

We found the factors 68,31,680 . The biggest common factor number is the GCF number.
So the greatest common factor 68,31,680 is 1.

Lets's calculate LCM of 22,34,495

Lowest Common Multiple of 22,34,495 using Common Division

2	22, 34, 495
11	11, 17, 495
	1, 17, 45

∴ So the LCM of the given numbers is 2 x 11 x 1 x 17 x 45 = 16830

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/16830

Therefore, the GCF of Fractions 68/22,31/34,680/495 is 1/16830

Least Common Multiple of 22,34,495 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 22,34,495 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(22,34,495) = 1

common factors(in case of two or more numbers have common factors) = 22

GCF(22,34,495) x common factors =1 x 22 = 22

LCM(22,34,495) = ( 22 × 34 × 495 ) / 22

LCM(22,34,495) = 370260 / 22

LCM(22,34,495) = 16830

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 68/22, 31/34, 680/495

1. What is the HCF of 68,31,680?

The HCF of 68,31,680 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 68/22, 31/34, 680/495?

Answer: GCF of Numerators as per given numbers 68/22, 31/34, 680/495 is

GCF of Numerators i.e. for 68,31,680 is 1

LCM of denominators i.e. for 22,34,495 is 16830.

Thus, GCF of Fractions is 1/16830.Finally, GCF of Fractions for 68/22, 31/34, 680/495 is 1/16830.