How to Find GCF of 29/22, 38/58, 109/51?

GCF of 29/22, 38/58, 109/51

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 29/22, 38/58, 109/51 i.e 1/32538 easily. The following is the detailed procedure to determine the greatest common factor of fractions 29/22, 38/58, 109/51.

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 29/22,38/58,109/51?

Given fractions are 29/22,38/58,109/51

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 29/22,38/58,109/51, numerators are 29,38,109

Denominators are 22,58,51

The GCF of 29,38,109 is 1 .

LCM of 22,58,51 is 32538.

The greatest common factor of 29/22,38/58,109/51 = [GCF of 29,38,109]/[LCM of 22,58,51]= 1/32538

Therefore, the GCF of 29/22,38/58,109/51 is 1/32538.

Greatest Common Factor of 29,38,109

To find the highest common factor of 29,38,109, we have to find the factors of both numbers and list the highest common factor.

The factors of 29 are 1, 29

The factors of 38 are 1, 2, 19, 38

The factors of 109 are 1, 109

The HCF of 29,38,109 is 1.

Lets's calculate GCF of 29,38,109

Greatest Common Factor (GCF) of 29,38,109 By Common Division

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

Greatest Common Factor of 29,38,109 By Matching Biggest Common Factor Method

Now, list down the factors of 29

1,29

Now, list down the factors of 38

1,2,19,38

Now, list down the factors of 109

1,109

Greatest Common Factor

We found the factors 29,38,109 . The biggest common factor number is the GCF number.
So the greatest common factor 29,38,109 is 1.

Lets's calculate LCM of 22,58,51

Lowest Common Multiple of 22,58,51 using Common Division

2	22, 58, 51
	11, 29, 51

∴ So the LCM of the given numbers is 2 x 11 x 29 x 51 = 32538

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/32538

Therefore, the GCF of Fractions 29/22,38/58,109/51 is 1/32538

Least Common Multiple of 22,58,51 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 22,58,51 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(22,58,51) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(22,58,51) x common factors =1 x 2 = 2

LCM(22,58,51) = ( 22 × 58 × 51 ) / 2

LCM(22,58,51) = 65076 / 2

LCM(22,58,51) = 32538

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FAQs on GCF of Fractions of 29/22, 38/58, 109/51

1. What is the HCF of 29,38,109?

The HCF of 29,38,109 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 29/22, 38/58, 109/51?

Answer: GCF of Numerators as per given numbers 29/22, 38/58, 109/51 is

GCF of Numerators i.e. for 29,38,109 is 1

LCM of denominators i.e. for 22,58,51 is 32538.

Thus, GCF of Fractions is 1/32538.Finally, GCF of Fractions for 29/22, 38/58, 109/51 is 1/32538.