How to Find GCF of 34/37, 22/67, 42/22?

GCF of 34/37, 22/67, 42/22

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 34/37, 22/67, 42/22 i.e 2/54538 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/37, 22/67, 42/22.

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 34/37,22/67,42/22?

Given fractions are 34/37,22/67,42/22

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 34/37,22/67,42/22, numerators are 34,22,42

Denominators are 37,67,22

The GCF of 34,22,42 is 2 .

LCM of 37,67,22 is 54538.

The greatest common factor of 34/37,22/67,42/22 = [GCF of 34,22,42]/[LCM of 37,67,22]= 2/54538

Therefore, the GCF of 34/37,22/67,42/22 is 2/54538.

Greatest Common Factor of 34,22,42

To find the highest common factor of 34,22,42, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 22 are 1, 2, 11, 22

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

The HCF of 34,22,42 is 2.

Lets's calculate GCF of 34,22,42

Greatest Common Factor (GCF) of 34,22,42 By Common Division

2	34, 22, 42
	17, 11, 21

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 34,22,42 By Matching Biggest Common Factor Method

Now, list down the factors of 34

1,2,17,34

Now, list down the factors of 22

1,2,11,22

Now, list down the factors of 42

1,2,3,6,7,14,21,42

Greatest Common Factor

We found the factors 34,22,42 . The biggest common factor number is the GCF number.
So the greatest common factor 34,22,42 is 2.

Lets's calculate LCM of 37,67,22

Lowest Common Multiple of 37,67,22 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 54538

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/54538

Therefore, the GCF of Fractions 34/37,22/67,42/22 is 2/54538

Least Common Multiple of 37,67,22 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 37,67,22 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(37,67,22) = 1

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

GCF(37,67,22) x common factors =1 x 1 = 1

LCM(37,67,22) = ( 37 × 67 × 22 ) / 1

LCM(37,67,22) = 54538 / 1

LCM(37,67,22) = 54538

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FAQs on GCF of Fractions of 34/37, 22/67, 42/22

1. What is the HCF of 34,22,42?

The HCF of 34,22,42 is 2

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 34/37, 22/67, 42/22?

Answer: GCF of Numerators as per given numbers 34/37, 22/67, 42/22 is

GCF of Numerators i.e. for 34,22,42 is 2

LCM of denominators i.e. for 37,67,22 is 54538.

Thus, GCF of Fractions is 2/54538.Finally, GCF of Fractions for 34/37, 22/67, 42/22 is 2/54538.