How to Find GCF of 13/42, 91/28, 34/72?

GCF of 13/42, 91/28, 34/72

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 13/42, 91/28, 34/72 i.e 1/504 easily. The following is the detailed procedure to determine the greatest common factor of fractions 13/42, 91/28, 34/72.

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 13/42,91/28,34/72?

Given fractions are 13/42,91/28,34/72

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 13/42,91/28,34/72, numerators are 13,91,34

Denominators are 42,28,72

The GCF of 13,91,34 is 1 .

LCM of 42,28,72 is 504.

The greatest common factor of 13/42,91/28,34/72 = [GCF of 13,91,34]/[LCM of 42,28,72]= 1/504

Therefore, the GCF of 13/42,91/28,34/72 is 1/504.

Greatest Common Factor of 13,91,34

To find the highest common factor of 13,91,34, we have to find the factors of both numbers and list the highest common factor.

The factors of 13 are 1, 13

The factors of 91 are 1, 7, 13, 91

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

The HCF of 13,91,34 is 1.

Lets's calculate GCF of 13,91,34

Greatest Common Factor (GCF) of 13,91,34 By Common Division

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

Greatest Common Factor of 13,91,34 By Matching Biggest Common Factor Method

Now, list down the factors of 13

1,13

Now, list down the factors of 91

1,7,13,91

Now, list down the factors of 34

1,2,17,34

Greatest Common Factor

We found the factors 13,91,34 . The biggest common factor number is the GCF number.
So the greatest common factor 13,91,34 is 1.

Lets's calculate LCM of 42,28,72

Lowest Common Multiple of 42,28,72 using Common Division

2	42, 28, 72
2	21, 14, 36
3	21, 7, 18
7	7, 7, 6
	1, 1, 6

∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 1 x 1 x 6 = 504

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/504

Therefore, the GCF of Fractions 13/42,91/28,34/72 is 1/504

Least Common Multiple of 42,28,72 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 42,28,72 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,28,72) = 2

common factors(in case of two or more numbers have common factors) = 84

GCF(42,28,72) x common factors =2 x 84 = 168

LCM(42,28,72) = ( 42 × 28 × 72 ) / 168

LCM(42,28,72) = 84672 / 168

LCM(42,28,72) = 504

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 13/42, 91/28, 34/72

1. What is the HCF of 13,91,34?

The HCF of 13,91,34 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 13/42, 91/28, 34/72?

Answer: GCF of Numerators as per given numbers 13/42, 91/28, 34/72 is

GCF of Numerators i.e. for 13,91,34 is 1

LCM of denominators i.e. for 42,28,72 is 504.

Thus, GCF of Fractions is 1/504.Finally, GCF of Fractions for 13/42, 91/28, 34/72 is 1/504.