How to Find GCF of 732/385, 704/342?

GCF of 732/385, 704/342

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 732/385, 704/342 i.e 4/131670 easily. The following is the detailed procedure to determine the greatest common factor of fractions 732/385, 704/342.

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 732/385,704/342?

Given fractions are 732/385,704/342

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 732/385,704/342, numerators are 732,704

Denominators are 385,342

The GCF of 732,704 is 4 .

LCM of 385,342 is 131670.

The greatest common factor of 732/385,704/342 = [GCF of 732,704]/[LCM of 385,342]= 4/131670

Therefore, the GCF of 732/385,704/342 is 4/131670.

Greatest Common Factor of 732,704

To find the highest common factor of 732,704, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 704 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, 704

The HCF of 732,704 is 4.

Lets's calculate GCF of 732,704

Greatest Common Factor (GCF) of 732,704 By Common Division

2	732, 704
2	366, 352
	183, 176

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

Greatest Common Factor of 732,704 By Matching Biggest Common Factor Method

Now, list down the factors of 732

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

Now, list down the factors of 704

1,2,4,8,11,16,22,32,44,64,88,176,352,704

Greatest Common Factor

We found the factors 732,704 . The biggest common factor number is the GCF number.
So the greatest common factor 732,704 is 4.

Lets's calculate LCM of 385,342

Lowest Common Multiple of 385,342 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 131670

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/131670

Therefore, the GCF of Fractions 732/385,704/342 is 4/131670

Least Common Multiple of 385,342 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 385,342 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(385,342) = 1

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

GCF(385,342) x common factors =1 x 1 = 1

LCM(385,342) = ( 385 × 342 ) / 1

LCM(385,342) = 131670 / 1

LCM(385,342) = 131670

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FAQs on GCF of Fractions of 732/385, 704/342

1. What is the HCF of 732,704?

The HCF of 732,704 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 732/385, 704/342?

Answer: GCF of Numerators as per given numbers 732/385, 704/342 is

GCF of Numerators i.e. for 732,704 is 4

LCM of denominators i.e. for 385,342 is 131670.

Thus, GCF of Fractions is 4/131670.Finally, GCF of Fractions for 732/385, 704/342 is 4/131670.