How to Find GCF of 14/69, 55/25, 782/442?

GCF of 14/69, 55/25, 782/442

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 14/69, 55/25, 782/442 i.e 1/762450 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/69, 55/25, 782/442.

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 14/69,55/25,782/442?

Given fractions are 14/69,55/25,782/442

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 14/69,55/25,782/442, numerators are 14,55,782

Denominators are 69,25,442

The GCF of 14,55,782 is 1 .

LCM of 69,25,442 is 762450.

The greatest common factor of 14/69,55/25,782/442 = [GCF of 14,55,782]/[LCM of 69,25,442]= 1/762450

Therefore, the GCF of 14/69,55/25,782/442 is 1/762450.

Greatest Common Factor of 14,55,782

To find the highest common factor of 14,55,782, we have to find the factors of both numbers and list the highest common factor.

The factors of 14 are 1, 2, 7, 14

The factors of 55 are 1, 5, 11, 55

The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782

The HCF of 14,55,782 is 1.

Lets's calculate GCF of 14,55,782

Greatest Common Factor (GCF) of 14,55,782 By Common Division

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

Greatest Common Factor of 14,55,782 By Matching Biggest Common Factor Method

Now, list down the factors of 14

1,2,7,14

Now, list down the factors of 55

1,5,11,55

Now, list down the factors of 782

1,2,17,23,34,46,391,782

Greatest Common Factor

We found the factors 14,55,782 . The biggest common factor number is the GCF number.
So the greatest common factor 14,55,782 is 1.

Lets's calculate LCM of 69,25,442

Lowest Common Multiple of 69,25,442 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 762450

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/762450

Therefore, the GCF of Fractions 14/69,55/25,782/442 is 1/762450

Least Common Multiple of 69,25,442 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 69,25,442 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(69,25,442) = 1

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

GCF(69,25,442) x common factors =1 x 1 = 1

LCM(69,25,442) = ( 69 × 25 × 442 ) / 1

LCM(69,25,442) = 762450 / 1

LCM(69,25,442) = 762450

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FAQs on GCF of Fractions of 14/69, 55/25, 782/442

1. What is the HCF of 14,55,782?

The HCF of 14,55,782 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 14/69, 55/25, 782/442?

Answer: GCF of Numerators as per given numbers 14/69, 55/25, 782/442 is

GCF of Numerators i.e. for 14,55,782 is 1

LCM of denominators i.e. for 69,25,442 is 762450.

Thus, GCF of Fractions is 1/762450.Finally, GCF of Fractions for 14/69, 55/25, 782/442 is 1/762450.