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GCF of 664/47, 414/314

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 664/47, 414/314 i.e 2/14758 easily. The following is the detailed procedure to determine the greatest common factor of fractions 664/47, 414/314.

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 664/47,414/314?

Given fractions are 664/47,414/314

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 664/47,414/314, numerators are 664,414

Denominators are 47,314

The GCF of 664,414 is 2 .

LCM of 47,314 is 14758.

The greatest common factor of 664/47,414/314 = [GCF of 664,414]/[LCM of 47,314]= 2/14758

Therefore, the GCF of 664/47,414/314 is 2/14758.

Greatest Common Factor of 664,414

To find the highest common factor of 664,414, we have to find the factors of both numbers and list the highest common factor.

The factors of 664 are 1, 2, 4, 8, 83, 166, 332, 664

The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414

The HCF of 664,414 is 2.

Lets's calculate GCF of 664,414

Greatest Common Factor (GCF) of 664,414 By Common Division

2 664, 414
332, 207

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

Greatest Common Factor of 664,414 By Matching Biggest Common Factor Method

Greatest Common Factor of 664,414 By Matching Biggest Common Factor Method

Now, list down the factors of 664

:

1,2,4,8,83,166,332,664

Now, list down the factors of 414

:

1,2,3,6,9,18,23,46,69,138,207,414

Greatest Common Factor

We found the factors 664,414 . The biggest common factor number is the GCF number.
So the greatest common factor 664,414 is 2.

Lets's calculate LCM of 47,314

Lowest Common Multiple of 47,314 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 14758

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/14758

Therefore, the GCF of Fractions 664/47,414/314 is 2/14758

Least Common Multiple of 47,314 with GCF Formula

Least Common Multiple of 47,314 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 47,314 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(47,314) = 1

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

GCF(47,314) x common factors =1 x 1 = 1

LCM(47,314) = ( 47 × 314 ) / 1

LCM(47,314) = 14758 / 1

LCM(47,314) = 14758


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FAQs on GCF of Fractions of 664/47, 414/314

1. What is the HCF of 664,414?

The HCF of 664,414 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 664/47, 414/314?

Answer: GCF of Numerators as per given numbers 664/47, 414/314 is

GCF of Numerators i.e. for 664,414 is 2

LCM of denominators i.e. for 47,314 is 14758.

Thus, GCF of Fractions is 2/14758.Finally, GCF of Fractions for 664/47, 414/314 is 2/14758.