How to Find GCF of 29/312, 67/840, 814/528?

GCF of 29/312, 67/840, 814/528

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 29/312, 67/840, 814/528 i.e 1/240240 easily. The following is the detailed procedure to determine the greatest common factor of fractions 29/312, 67/840, 814/528.

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 29/312,67/840,814/528?

Given fractions are 29/312,67/840,814/528

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 29/312,67/840,814/528, numerators are 29,67,814

Denominators are 312,840,528

The GCF of 29,67,814 is 1 .

LCM of 312,840,528 is 240240.

The greatest common factor of 29/312,67/840,814/528 = [GCF of 29,67,814]/[LCM of 312,840,528]= 1/240240

Therefore, the GCF of 29/312,67/840,814/528 is 1/240240.

Greatest Common Factor of 29,67,814

To find the highest common factor of 29,67,814, we have to find the factors of both numbers and list the highest common factor.

The factors of 29 are 1, 29

The factors of 67 are 1, 67

The factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814

The HCF of 29,67,814 is 1.

Lets's calculate GCF of 29,67,814

Greatest Common Factor (GCF) of 29,67,814 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 29,67,814 By Matching Biggest Common Factor Method

Now, list down the factors of 29

1,29

Now, list down the factors of 67

1,67

Now, list down the factors of 814

1,2,11,22,37,74,407,814

Greatest Common Factor

We found the factors 29,67,814 . The biggest common factor number is the GCF number.
So the greatest common factor 29,67,814 is 1.

Lets's calculate LCM of 312,840,528

Lowest Common Multiple of 312,840,528 using Common Division

2	312, 840, 528
2	156, 420, 264
2	78, 210, 132
3	39, 105, 66
	13, 35, 22

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 13 x 35 x 22 = 240240

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/240240

Therefore, the GCF of Fractions 29/312,67/840,814/528 is 1/240240

Least Common Multiple of 312,840,528 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 312,840,528 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(312,840,528) = 24

common factors(in case of two or more numbers have common factors) = 24

GCF(312,840,528) x common factors =24 x 24 = 576

LCM(312,840,528) = ( 312 × 840 × 528 ) / 576

LCM(312,840,528) = 138378240 / 576

LCM(312,840,528) = 240240

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 29/312, 67/840, 814/528

1. What is the HCF of 29,67,814?

The HCF of 29,67,814 is 1

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 29/312, 67/840, 814/528?

Answer: GCF of Numerators as per given numbers 29/312, 67/840, 814/528 is

GCF of Numerators i.e. for 29,67,814 is 1

LCM of denominators i.e. for 312,840,528 is 240240.

Thus, GCF of Fractions is 1/240240.Finally, GCF of Fractions for 29/312, 67/840, 814/528 is 1/240240.