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GCF of 732/67, 274/346

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 732/67, 274/346 i.e 2/23182 easily. The following is the detailed procedure to determine the greatest common factor of fractions 732/67, 274/346.

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 732/67,274/346?

Given fractions are 732/67,274/346

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 732/67,274/346, numerators are 732,274

Denominators are 67,346

The GCF of 732,274 is 2 .

LCM of 67,346 is 23182.

The greatest common factor of 732/67,274/346 = [GCF of 732,274]/[LCM of 67,346]= 2/23182

Therefore, the GCF of 732/67,274/346 is 2/23182.

Greatest Common Factor of 732,274

To find the highest common factor of 732,274, 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 274 are 1, 2, 137, 274

The HCF of 732,274 is 2.

Lets's calculate GCF of 732,274

Greatest Common Factor (GCF) of 732,274 By Common Division

2 732, 274
366, 137

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

Greatest Common Factor of 732,274 By Matching Biggest Common Factor Method

Greatest Common Factor of 732,274 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 274

:

1,2,137,274

Greatest Common Factor

We found the factors 732,274 . The biggest common factor number is the GCF number.
So the greatest common factor 732,274 is 2.

Lets's calculate LCM of 67,346

Lowest Common Multiple of 67,346 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 23182

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/23182

Therefore, the GCF of Fractions 732/67,274/346 is 2/23182

Least Common Multiple of 67,346 with GCF Formula

Least Common Multiple of 67,346 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 67,346 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(67,346) = 1

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

GCF(67,346) x common factors =1 x 1 = 1

LCM(67,346) = ( 67 × 346 ) / 1

LCM(67,346) = 23182 / 1

LCM(67,346) = 23182


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FAQs on GCF of Fractions of 732/67, 274/346

1. What is the HCF of 732,274?

The HCF of 732,274 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 732/67, 274/346?

Answer: GCF of Numerators as per given numbers 732/67, 274/346 is

GCF of Numerators i.e. for 732,274 is 2

LCM of denominators i.e. for 67,346 is 23182.

Thus, GCF of Fractions is 2/23182.Finally, GCF of Fractions for 732/67, 274/346 is 2/23182.