How to Find GCF of 34/67, 931/68, 379/614?

GCF of 34/67, 931/68, 379/614

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 34/67, 931/68, 379/614 i.e 1/1398692 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/67, 931/68, 379/614.

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 34/67,931/68,379/614?

Given fractions are 34/67,931/68,379/614

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 34/67,931/68,379/614, numerators are 34,931,379

Denominators are 67,68,614

The GCF of 34,931,379 is 1 .

LCM of 67,68,614 is 1398692.

The greatest common factor of 34/67,931/68,379/614 = [GCF of 34,931,379]/[LCM of 67,68,614]= 1/1398692

Therefore, the GCF of 34/67,931/68,379/614 is 1/1398692.

Greatest Common Factor of 34,931,379

To find the highest common factor of 34,931,379, 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 931 are 1, 7, 19, 49, 133, 931

The factors of 379 are 1, 379

The HCF of 34,931,379 is 1.

Lets's calculate GCF of 34,931,379

Greatest Common Factor (GCF) of 34,931,379 By Common Division

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

Greatest Common Factor of 34,931,379 By Matching Biggest Common Factor Method

Now, list down the factors of 34

1,2,17,34

Now, list down the factors of 931

1,7,19,49,133,931

Now, list down the factors of 379

1,379

Greatest Common Factor

We found the factors 34,931,379 . The biggest common factor number is the GCF number.
So the greatest common factor 34,931,379 is 1.

Lets's calculate LCM of 67,68,614

Lowest Common Multiple of 67,68,614 using Common Division

2	67, 68, 614
	67, 34, 307

∴ So the LCM of the given numbers is 2 x 67 x 34 x 307 = 1398692

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1398692

Therefore, the GCF of Fractions 34/67,931/68,379/614 is 1/1398692

Least Common Multiple of 67,68,614 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 67,68,614 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(67,68,614) = 1

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

GCF(67,68,614) x common factors =1 x 2 = 2

LCM(67,68,614) = ( 67 × 68 × 614 ) / 2

LCM(67,68,614) = 2797384 / 2

LCM(67,68,614) = 1398692

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FAQs on GCF of Fractions of 34/67, 931/68, 379/614

1. What is the HCF of 34,931,379?

The HCF of 34,931,379 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 34/67, 931/68, 379/614?

Answer: GCF of Numerators as per given numbers 34/67, 931/68, 379/614 is

GCF of Numerators i.e. for 34,931,379 is 1

LCM of denominators i.e. for 67,68,614 is 1398692.

Thus, GCF of Fractions is 1/1398692.Finally, GCF of Fractions for 34/67, 931/68, 379/614 is 1/1398692.