How to Find GCF of 66/340, 8412/1174?

GCF of 66/340, 8412/1174

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 66/340, 8412/1174 i.e 6/199580 easily. The following is the detailed procedure to determine the greatest common factor of fractions 66/340, 8412/1174.

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 66/340,8412/1174?

Given fractions are 66/340,8412/1174

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 66/340,8412/1174, numerators are 66,8412

Denominators are 340,1174

The GCF of 66,8412 is 6 .

LCM of 340,1174 is 199580.

The greatest common factor of 66/340,8412/1174 = [GCF of 66,8412]/[LCM of 340,1174]= 6/199580

Therefore, the GCF of 66/340,8412/1174 is 6/199580.

Greatest Common Factor of 66,8412

To find the highest common factor of 66,8412, 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 8412 are 1, 2, 3, 4, 6, 12, 701, 1402, 2103, 2804, 4206, 8412

The HCF of 66,8412 is 6.

Lets's calculate GCF of 66,8412

Greatest Common Factor (GCF) of 66,8412 By Common Division

2	66, 8412
3	33, 4206
	11, 1402

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 66,8412 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 8412

1,2,3,4,6,12,701,1402,2103,2804,4206,8412

Greatest Common Factor

We found the factors 66,8412 . The biggest common factor number is the GCF number.
So the greatest common factor 66,8412 is 6.

Lets's calculate LCM of 340,1174

Lowest Common Multiple of 340,1174 using Common Division

2	340, 1174
	170, 587

∴ So the LCM of the given numbers is 2 x 170 x 587 = 199580

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/199580

Therefore, the GCF of Fractions 66/340,8412/1174 is 6/199580

Least Common Multiple of 340,1174 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 340,1174 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(340,1174) = 2

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

GCF(340,1174) x common factors =2 x 1 = 2

LCM(340,1174) = ( 340 × 1174 ) / 2

LCM(340,1174) = 399160 / 2

LCM(340,1174) = 199580

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FAQs on GCF of Fractions of 66/340, 8412/1174

1. What is the HCF of 66,8412?

The HCF of 66,8412 is 6

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 66/340, 8412/1174?

Answer: GCF of Numerators as per given numbers 66/340, 8412/1174 is

GCF of Numerators i.e. for 66,8412 is 6

LCM of denominators i.e. for 340,1174 is 199580.

Thus, GCF of Fractions is 6/199580.Finally, GCF of Fractions for 66/340, 8412/1174 is 6/199580.