How to Find GCF of 40/132, 70/164, 624/940?

GCF of 40/132, 70/164, 624/940

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 40/132, 70/164, 624/940 i.e 2/1271820 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/132, 70/164, 624/940.

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 40/132,70/164,624/940?

Given fractions are 40/132,70/164,624/940

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 40/132,70/164,624/940, numerators are 40,70,624

Denominators are 132,164,940

The GCF of 40,70,624 is 2 .

LCM of 132,164,940 is 1271820.

The greatest common factor of 40/132,70/164,624/940 = [GCF of 40,70,624]/[LCM of 132,164,940]= 2/1271820

Therefore, the GCF of 40/132,70/164,624/940 is 2/1271820.

Greatest Common Factor of 40,70,624

To find the highest common factor of 40,70,624, 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 70 are 1, 2, 5, 7, 10, 14, 35, 70

The factors of 624 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624

The HCF of 40,70,624 is 2.

Lets's calculate GCF of 40,70,624

Greatest Common Factor (GCF) of 40,70,624 By Common Division

2	40, 70, 624
	20, 35, 312

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

Greatest Common Factor of 40,70,624 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 70

1,2,5,7,10,14,35,70

Now, list down the factors of 624

1,2,3,4,6,8,12,13,16,24,26,39,48,52,78,104,156,208,312,624

Greatest Common Factor

We found the factors 40,70,624 . The biggest common factor number is the GCF number.
So the greatest common factor 40,70,624 is 2.

Lets's calculate LCM of 132,164,940

Lowest Common Multiple of 132,164,940 using Common Division

2	132, 164, 940
2	66, 82, 470
	33, 41, 235

∴ So the LCM of the given numbers is 2 x 2 x 33 x 41 x 235 = 1271820

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1271820

Therefore, the GCF of Fractions 40/132,70/164,624/940 is 2/1271820

Least Common Multiple of 132,164,940 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 132,164,940 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(132,164,940) = 4

common factors(in case of two or more numbers have common factors) = 4

GCF(132,164,940) x common factors =4 x 4 = 16

LCM(132,164,940) = ( 132 × 164 × 940 ) / 16

LCM(132,164,940) = 20349120 / 16

LCM(132,164,940) = 1271820

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 40/132, 70/164, 624/940

1. What is the HCF of 40,70,624?

The HCF of 40,70,624 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 40/132, 70/164, 624/940?

Answer: GCF of Numerators as per given numbers 40/132, 70/164, 624/940 is

GCF of Numerators i.e. for 40,70,624 is 2

LCM of denominators i.e. for 132,164,940 is 1271820.

Thus, GCF of Fractions is 2/1271820.Finally, GCF of Fractions for 40/132, 70/164, 624/940 is 2/1271820.