How to Find GCF of 34/78, 70/14, 17/59?

GCF of 34/78, 70/14, 17/59

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 34/78, 70/14, 17/59 i.e 1/32214 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/78, 70/14, 17/59.

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 34/78,70/14,17/59?

Given fractions are 34/78,70/14,17/59

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 34/78,70/14,17/59, numerators are 34,70,17

Denominators are 78,14,59

The GCF of 34,70,17 is 1 .

LCM of 78,14,59 is 32214.

The greatest common factor of 34/78,70/14,17/59 = [GCF of 34,70,17]/[LCM of 78,14,59]= 1/32214

Therefore, the GCF of 34/78,70/14,17/59 is 1/32214.

Greatest Common Factor of 34,70,17

To find the highest common factor of 34,70,17, 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 70 are 1, 2, 5, 7, 10, 14, 35, 70

The factors of 17 are 1, 17

The HCF of 34,70,17 is 1.

Lets's calculate GCF of 34,70,17

Greatest Common Factor (GCF) of 34,70,17 By Common Division

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

Greatest Common Factor of 34,70,17 By Matching Biggest Common Factor Method

Now, list down the factors of 34

1,2,17,34

Now, list down the factors of 70

1,2,5,7,10,14,35,70

Now, list down the factors of 17

1,17

Greatest Common Factor

We found the factors 34,70,17 . The biggest common factor number is the GCF number.
So the greatest common factor 34,70,17 is 1.

Lets's calculate LCM of 78,14,59

Lowest Common Multiple of 78,14,59 using Common Division

2	78, 14, 59
	39, 7, 59

∴ So the LCM of the given numbers is 2 x 39 x 7 x 59 = 32214

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/32214

Therefore, the GCF of Fractions 34/78,70/14,17/59 is 1/32214

Least Common Multiple of 78,14,59 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 78,14,59 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,14,59) = 1

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

GCF(78,14,59) x common factors =1 x 2 = 2

LCM(78,14,59) = ( 78 × 14 × 59 ) / 2

LCM(78,14,59) = 64428 / 2

LCM(78,14,59) = 32214

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FAQs on GCF of Fractions of 34/78, 70/14, 17/59

1. What is the HCF of 34,70,17?

The HCF of 34,70,17 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 34/78, 70/14, 17/59?

Answer: GCF of Numerators as per given numbers 34/78, 70/14, 17/59 is

GCF of Numerators i.e. for 34,70,17 is 1

LCM of denominators i.e. for 78,14,59 is 32214.

Thus, GCF of Fractions is 1/32214.Finally, GCF of Fractions for 34/78, 70/14, 17/59 is 1/32214.