How to Find GCF of 66/154, 6076/8140?

GCF of 66/154, 6076/8140

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 66/154, 6076/8140 i.e 2/56980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 66/154, 6076/8140.

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 66/154,6076/8140?

Given fractions are 66/154,6076/8140

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 66/154,6076/8140, numerators are 66,6076

Denominators are 154,8140

The GCF of 66,6076 is 2 .

LCM of 154,8140 is 56980.

The greatest common factor of 66/154,6076/8140 = [GCF of 66,6076]/[LCM of 154,8140]= 2/56980

Therefore, the GCF of 66/154,6076/8140 is 2/56980.

Greatest Common Factor of 66,6076

To find the highest common factor of 66,6076, we have to find the factors of both numbers and list the highest common factor.

The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66

The factors of 6076 are 1, 2, 4, 7, 14, 28, 31, 49, 62, 98, 124, 196, 217, 434, 868, 1519, 3038, 6076

The HCF of 66,6076 is 2.

Lets's calculate GCF of 66,6076

Greatest Common Factor (GCF) of 66,6076 By Common Division

2	66, 6076
	33, 3038

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

Greatest Common Factor of 66,6076 By Matching Biggest Common Factor Method

Now, list down the factors of 66

1,2,3,6,11,22,33,66

Now, list down the factors of 6076

1,2,4,7,14,28,31,49,62,98,124,196,217,434,868,1519,3038,6076

Greatest Common Factor

We found the factors 66,6076 . The biggest common factor number is the GCF number.
So the greatest common factor 66,6076 is 2.

Lets's calculate LCM of 154,8140

Lowest Common Multiple of 154,8140 using Common Division

2	154, 8140
11	77, 4070
	7, 370

∴ So the LCM of the given numbers is 2 x 11 x 7 x 370 = 56980

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/56980

Therefore, the GCF of Fractions 66/154,6076/8140 is 2/56980

Least Common Multiple of 154,8140 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 154,8140 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(154,8140) = 22

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

GCF(154,8140) x common factors =22 x 1 = 22

LCM(154,8140) = ( 154 × 8140 ) / 22

LCM(154,8140) = 1253560 / 22

LCM(154,8140) = 56980

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FAQs on GCF of Fractions of 66/154, 6076/8140

1. What is the HCF of 66,6076?

The HCF of 66,6076 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 66/154, 6076/8140?

Answer: GCF of Numerators as per given numbers 66/154, 6076/8140 is

GCF of Numerators i.e. for 66,6076 is 2

LCM of denominators i.e. for 154,8140 is 56980.

Thus, GCF of Fractions is 2/56980.Finally, GCF of Fractions for 66/154, 6076/8140 is 2/56980.