How to Find GCF of 40/10, 668/11, 314/117?

GCF of 40/10, 668/11, 314/117

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 40/10, 668/11, 314/117 i.e 2/12870 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/10, 668/11, 314/117.

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 40/10,668/11,314/117?

Given fractions are 40/10,668/11,314/117

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 40/10,668/11,314/117, numerators are 40,668,314

Denominators are 10,11,117

The GCF of 40,668,314 is 2 .

LCM of 10,11,117 is 12870.

The greatest common factor of 40/10,668/11,314/117 = [GCF of 40,668,314]/[LCM of 10,11,117]= 2/12870

Therefore, the GCF of 40/10,668/11,314/117 is 2/12870.

Greatest Common Factor of 40,668,314

To find the highest common factor of 40,668,314, we have to find the factors of both numbers and list the highest common factor.

The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40

The factors of 668 are 1, 2, 4, 167, 334, 668

The factors of 314 are 1, 2, 157, 314

The HCF of 40,668,314 is 2.

Lets's calculate GCF of 40,668,314

Greatest Common Factor (GCF) of 40,668,314 By Common Division

2	40, 668, 314
	20, 334, 157

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

Greatest Common Factor of 40,668,314 By Matching Biggest Common Factor Method

Now, list down the factors of 40

1,2,4,5,8,10,20,40

Now, list down the factors of 668

1,2,4,167,334,668

Now, list down the factors of 314

1,2,157,314

Greatest Common Factor

We found the factors 40,668,314 . The biggest common factor number is the GCF number.
So the greatest common factor 40,668,314 is 2.

Lets's calculate LCM of 10,11,117

Lowest Common Multiple of 10,11,117 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 12870

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/12870

Therefore, the GCF of Fractions 40/10,668/11,314/117 is 2/12870

Least Common Multiple of 10,11,117 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 10,11,117 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(10,11,117) = 1

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

GCF(10,11,117) x common factors =1 x 1 = 1

LCM(10,11,117) = ( 10 × 11 × 117 ) / 1

LCM(10,11,117) = 12870 / 1

LCM(10,11,117) = 12870

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FAQs on GCF of Fractions of 40/10, 668/11, 314/117

1. What is the HCF of 40,668,314?

The HCF of 40,668,314 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 40/10, 668/11, 314/117?

Answer: GCF of Numerators as per given numbers 40/10, 668/11, 314/117 is

GCF of Numerators i.e. for 40,668,314 is 2

LCM of denominators i.e. for 10,11,117 is 12870.

Thus, GCF of Fractions is 2/12870.Finally, GCF of Fractions for 40/10, 668/11, 314/117 is 2/12870.