How to Find GCF of 274/830, 402/556, 469/782?

GCF of 274/830, 402/556, 469/782

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 274/830, 402/556, 469/782 i.e 1/90219340 easily. The following is the detailed procedure to determine the greatest common factor of fractions 274/830, 402/556, 469/782.

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 274/830,402/556,469/782?

Given fractions are 274/830,402/556,469/782

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 274/830,402/556,469/782, numerators are 274,402,469

Denominators are 830,556,782

The GCF of 274,402,469 is 1 .

LCM of 830,556,782 is 90219340.

The greatest common factor of 274/830,402/556,469/782 = [GCF of 274,402,469]/[LCM of 830,556,782]= 1/90219340

Therefore, the GCF of 274/830,402/556,469/782 is 1/90219340.

Greatest Common Factor of 274,402,469

To find the highest common factor of 274,402,469, we have to find the factors of both numbers and list the highest common factor.

The factors of 274 are 1, 2, 137, 274

The factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402

The factors of 469 are 1, 7, 67, 469

The HCF of 274,402,469 is 1.

Lets's calculate GCF of 274,402,469

Greatest Common Factor (GCF) of 274,402,469 By Common Division

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

Greatest Common Factor of 274,402,469 By Matching Biggest Common Factor Method

Now, list down the factors of 274

1,2,137,274

Now, list down the factors of 402

1,2,3,6,67,134,201,402

Now, list down the factors of 469

1,7,67,469

Greatest Common Factor

We found the factors 274,402,469 . The biggest common factor number is the GCF number.
So the greatest common factor 274,402,469 is 1.

Lets's calculate LCM of 830,556,782

Lowest Common Multiple of 830,556,782 using Common Division

2	830, 556, 782
	415, 278, 391

∴ So the LCM of the given numbers is 2 x 415 x 278 x 391 = 90219340

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/90219340

Therefore, the GCF of Fractions 274/830,402/556,469/782 is 1/90219340

Least Common Multiple of 830,556,782 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 830,556,782 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(830,556,782) = 2

common factors(in case of two or more numbers have common factors) = 2

GCF(830,556,782) x common factors =2 x 2 = 4

LCM(830,556,782) = ( 830 × 556 × 782 ) / 4

LCM(830,556,782) = 360877360 / 4

LCM(830,556,782) = 90219340

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 274/830, 402/556, 469/782

1. What is the HCF of 274,402,469?

The HCF of 274,402,469 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 274/830, 402/556, 469/782?

Answer: GCF of Numerators as per given numbers 274/830, 402/556, 469/782 is

GCF of Numerators i.e. for 274,402,469 is 1

LCM of denominators i.e. for 830,556,782 is 90219340.

Thus, GCF of Fractions is 1/90219340.Finally, GCF of Fractions for 274/830, 402/556, 469/782 is 1/90219340.