How to Find GCF of 36/67, 58/78, 467/416?

GCF of 36/67, 58/78, 467/416

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 36/67, 58/78, 467/416 i.e 1/83616 easily. The following is the detailed procedure to determine the greatest common factor of fractions 36/67, 58/78, 467/416.

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 36/67,58/78,467/416?

Given fractions are 36/67,58/78,467/416

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 36/67,58/78,467/416, numerators are 36,58,467

Denominators are 67,78,416

The GCF of 36,58,467 is 1 .

LCM of 67,78,416 is 83616.

The greatest common factor of 36/67,58/78,467/416 = [GCF of 36,58,467]/[LCM of 67,78,416]= 1/83616

Therefore, the GCF of 36/67,58/78,467/416 is 1/83616.

Greatest Common Factor of 36,58,467

To find the highest common factor of 36,58,467, we have to find the factors of both numbers and list the highest common factor.

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36

The factors of 58 are 1, 2, 29, 58

The factors of 467 are 1, 467

The HCF of 36,58,467 is 1.

Lets's calculate GCF of 36,58,467

Greatest Common Factor (GCF) of 36,58,467 By Common Division

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

Greatest Common Factor of 36,58,467 By Matching Biggest Common Factor Method

Now, list down the factors of 36

1,2,3,4,6,9,12,18,36

Now, list down the factors of 58

1,2,29,58

Now, list down the factors of 467

1,467

Greatest Common Factor

We found the factors 36,58,467 . The biggest common factor number is the GCF number.
So the greatest common factor 36,58,467 is 1.

Lets's calculate LCM of 67,78,416

Lowest Common Multiple of 67,78,416 using Common Division

2	67, 78, 416
13	67, 39, 208
	67, 3, 16

∴ So the LCM of the given numbers is 2 x 13 x 67 x 3 x 16 = 83616

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/83616

Therefore, the GCF of Fractions 36/67,58/78,467/416 is 1/83616

Least Common Multiple of 67,78,416 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 67,78,416 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(67,78,416) = 1

common factors(in case of two or more numbers have common factors) = 26

GCF(67,78,416) x common factors =1 x 26 = 26

LCM(67,78,416) = ( 67 × 78 × 416 ) / 26

LCM(67,78,416) = 2174016 / 26

LCM(67,78,416) = 83616

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FAQs on GCF of Fractions of 36/67, 58/78, 467/416

1. What is the HCF of 36,58,467?

The HCF of 36,58,467 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 36/67, 58/78, 467/416?

Answer: GCF of Numerators as per given numbers 36/67, 58/78, 467/416 is

GCF of Numerators i.e. for 36,58,467 is 1

LCM of denominators i.e. for 67,78,416 is 83616.

Thus, GCF of Fractions is 1/83616.Finally, GCF of Fractions for 36/67, 58/78, 467/416 is 1/83616.