How to Find GCF of 74/969, 65/136, 719/712?

GCF of 74/969, 65/136, 719/712

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 74/969, 65/136, 719/712 i.e 1/689928 easily. The following is the detailed procedure to determine the greatest common factor of fractions 74/969, 65/136, 719/712.

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 74/969,65/136,719/712?

Given fractions are 74/969,65/136,719/712

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 74/969,65/136,719/712, numerators are 74,65,719

Denominators are 969,136,712

The GCF of 74,65,719 is 1 .

LCM of 969,136,712 is 689928.

The greatest common factor of 74/969,65/136,719/712 = [GCF of 74,65,719]/[LCM of 969,136,712]= 1/689928

Therefore, the GCF of 74/969,65/136,719/712 is 1/689928.

Greatest Common Factor of 74,65,719

To find the highest common factor of 74,65,719, we have to find the factors of both numbers and list the highest common factor.

The factors of 74 are 1, 2, 37, 74

The factors of 65 are 1, 5, 13, 65

The factors of 719 are 1, 719

The HCF of 74,65,719 is 1.

Lets's calculate GCF of 74,65,719

Greatest Common Factor (GCF) of 74,65,719 By Common Division

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

Greatest Common Factor of 74,65,719 By Matching Biggest Common Factor Method

Now, list down the factors of 74

1,2,37,74

Now, list down the factors of 65

1,5,13,65

Now, list down the factors of 719

1,719

Greatest Common Factor

We found the factors 74,65,719 . The biggest common factor number is the GCF number.
So the greatest common factor 74,65,719 is 1.

Lets's calculate LCM of 969,136,712

Lowest Common Multiple of 969,136,712 using Common Division

2	969, 136, 712
2	969, 68, 356
2	969, 34, 178
17	969, 17, 89
	57, 1, 89

∴ So the LCM of the given numbers is 2 x 2 x 2 x 17 x 57 x 1 x 89 = 689928

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/689928

Therefore, the GCF of Fractions 74/969,65/136,719/712 is 1/689928

Least Common Multiple of 969,136,712 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 969,136,712 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(969,136,712) = 1

common factors(in case of two or more numbers have common factors) = 136

GCF(969,136,712) x common factors =1 x 136 = 136

LCM(969,136,712) = ( 969 × 136 × 712 ) / 136

LCM(969,136,712) = 93830208 / 136

LCM(969,136,712) = 689928

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 74/969, 65/136, 719/712

1. What is the HCF of 74,65,719?

The HCF of 74,65,719 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 74/969, 65/136, 719/712?

Answer: GCF of Numerators as per given numbers 74/969, 65/136, 719/712 is

GCF of Numerators i.e. for 74,65,719 is 1

LCM of denominators i.e. for 969,136,712 is 689928.

Thus, GCF of Fractions is 1/689928.Finally, GCF of Fractions for 74/969, 65/136, 719/712 is 1/689928.