How to Find GCF of 36/49, 61/74, 83/64, 34/39?

GCF of 36/49, 61/74, 83/64, 34/39

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 36/49, 61/74, 83/64, 34/39 i.e 1/4525248 easily. The following is the detailed procedure to determine the greatest common factor of fractions 36/49, 61/74, 83/64, 34/39.

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 36/49,61/74,83/64,34/39?

Given fractions are 36/49,61/74,83/64,34/39

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 36/49,61/74,83/64,34/39, numerators are 36,61,83,34

Denominators are 49,74,64,39

The GCF of 36,61,83,34 is 1 .

LCM of 49,74,64,39 is 4525248.

The greatest common factor of 36/49,61/74,83/64,34/39 = [GCF of 36,61,83,34]/[LCM of 49,74,64,39]= 1/4525248

Therefore, the GCF of 36/49,61/74,83/64,34/39 is 1/4525248.

Greatest Common Factor of 36,61,83,34

To find the highest common factor of 36,61,83,34, 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 61 are 1, 61

The factors of 83 are 1, 83

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

The HCF of 36,61,83,34 is 1.

Lets's calculate GCF of 36,61,83,34

Greatest Common Factor (GCF) of 36,61,83,34 By Common Division

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

Greatest Common Factor of 36,61,83,34 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 61

1,61

Now, list down the factors of 83

1,83

Now, list down the factors of 34

1,2,17,34

Greatest Common Factor

We found the factors 36,61,83,34 . The biggest common factor number is the GCF number.
So the greatest common factor 36,61,83,34 is 1.

Lets's calculate LCM of 49,74,64,39

Lowest Common Multiple of 49,74,64,39 using Common Division

2	49, 74, 64, 39
	49, 37, 32, 39

∴ So the LCM of the given numbers is 2 x 49 x 37 x 32 x 39 = 4525248

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4525248

Therefore, the GCF of Fractions 36/49,61/74,83/64,34/39 is 1/4525248

Least Common Multiple of 49,74,64,39 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 49,74,64,39 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(49,74,64,39) = 1

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

GCF(49,74,64,39) x common factors =1 x 2 = 2

LCM(49,74,64,39) = ( 49 × 74 × 64 × 39 ) / 2

LCM(49,74,64,39) = 9050496 / 2

LCM(49,74,64,39) = 4525248

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 36/49, 61/74, 83/64, 34/39

1. What is the HCF of 36,61,83,34?

The HCF of 36,61,83,34 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 36/49, 61/74, 83/64, 34/39?

Answer: GCF of Numerators as per given numbers 36/49, 61/74, 83/64, 34/39 is

GCF of Numerators i.e. for 36,61,83,34 is 1

LCM of denominators i.e. for 49,74,64,39 is 4525248.

Thus, GCF of Fractions is 1/4525248.Finally, GCF of Fractions for 36/49, 61/74, 83/64, 34/39 is 1/4525248.