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GCF of 374/456, 206/180

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 374/456, 206/180 i.e 2/6840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 374/456, 206/180.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 374/456,206/180?

Given fractions are 374/456,206/180

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 374/456,206/180, numerators are 374,206

Denominators are 456,180

The GCF of 374,206 is 2 .

LCM of 456,180 is 6840.

The greatest common factor of 374/456,206/180 = [GCF of 374,206]/[LCM of 456,180]= 2/6840

Therefore, the GCF of 374/456,206/180 is 2/6840.

Greatest Common Factor of 374,206

To find the highest common factor of 374,206, we have to find the factors of both numbers and list the highest common factor.

The factors of 374 are 1, 2, 11, 17, 22, 34, 187, 374

The factors of 206 are 1, 2, 103, 206

The HCF of 374,206 is 2.

Lets's calculate GCF of 374,206

Greatest Common Factor (GCF) of 374,206 By Common Division

2 374, 206
187, 103

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

Greatest Common Factor of 374,206 By Matching Biggest Common Factor Method

Greatest Common Factor of 374,206 By Matching Biggest Common Factor Method

Now, list down the factors of 374

:

1,2,11,17,22,34,187,374

Now, list down the factors of 206

:

1,2,103,206

Greatest Common Factor

We found the factors 374,206 . The biggest common factor number is the GCF number.
So the greatest common factor 374,206 is 2.

Lets's calculate LCM of 456,180

Lowest Common Multiple of 456,180 using Common Division

2 456, 180
2 228, 90
3 114, 45
38, 15

∴ So the LCM of the given numbers is 2 x 2 x 3 x 38 x 15 = 6840

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/6840

Therefore, the GCF of Fractions 374/456,206/180 is 2/6840

Least Common Multiple of 456,180 with GCF Formula

Least Common Multiple of 456,180 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 456,180 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(456,180) = 12

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

GCF(456,180) x common factors =12 x 1 = 12

LCM(456,180) = ( 456 × 180 ) / 12

LCM(456,180) = 82080 / 12

LCM(456,180) = 6840


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FAQs on GCF of Fractions of 374/456, 206/180

1. What is the HCF of 374,206?

The HCF of 374,206 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 374/456, 206/180?

Answer: GCF of Numerators as per given numbers 374/456, 206/180 is

GCF of Numerators i.e. for 374,206 is 2

LCM of denominators i.e. for 456,180 is 6840.

Thus, GCF of Fractions is 2/6840.Finally, GCF of Fractions for 374/456, 206/180 is 2/6840.