How to Find GCF of 364/428, 732/164?

GCF of 364/428, 732/164

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 364/428, 732/164 i.e 4/17548 easily. The following is the detailed procedure to determine the greatest common factor of fractions 364/428, 732/164.

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 364/428,732/164?

Given fractions are 364/428,732/164

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 364/428,732/164, numerators are 364,732

Denominators are 428,164

The GCF of 364,732 is 4 .

LCM of 428,164 is 17548.

The greatest common factor of 364/428,732/164 = [GCF of 364,732]/[LCM of 428,164]= 4/17548

Therefore, the GCF of 364/428,732/164 is 4/17548.

Greatest Common Factor of 364,732

To find the highest common factor of 364,732, we have to find the factors of both numbers and list the highest common factor.

The factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364

The factors of 732 are 1, 2, 3, 4, 6, 12, 61, 122, 183, 244, 366, 732

The HCF of 364,732 is 4.

Lets's calculate GCF of 364,732

Greatest Common Factor (GCF) of 364,732 By Common Division

2	364, 732
2	182, 366
	91, 183

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 364,732 By Matching Biggest Common Factor Method

Now, list down the factors of 364

1,2,4,7,13,14,26,28,52,91,182,364

Now, list down the factors of 732

1,2,3,4,6,12,61,122,183,244,366,732

Greatest Common Factor

We found the factors 364,732 . The biggest common factor number is the GCF number.
So the greatest common factor 364,732 is 4.

Lets's calculate LCM of 428,164

Lowest Common Multiple of 428,164 using Common Division

2	428, 164
2	214, 82
	107, 41

∴ So the LCM of the given numbers is 2 x 2 x 107 x 41 = 17548

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/17548

Therefore, the GCF of Fractions 364/428,732/164 is 4/17548

Least Common Multiple of 428,164 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 428,164 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(428,164) = 4

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

GCF(428,164) x common factors =4 x 1 = 4

LCM(428,164) = ( 428 × 164 ) / 4

LCM(428,164) = 70192 / 4

LCM(428,164) = 17548

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FAQs on GCF of Fractions of 364/428, 732/164

1. What is the HCF of 364,732?

The HCF of 364,732 is 4

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 364/428, 732/164?

Answer: GCF of Numerators as per given numbers 364/428, 732/164 is

GCF of Numerators i.e. for 364,732 is 4

LCM of denominators i.e. for 428,164 is 17548.

Thus, GCF of Fractions is 4/17548.Finally, GCF of Fractions for 364/428, 732/164 is 4/17548.