How to Find GCF of 532/786, 419/768?

GCF of 532/786, 419/768

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 532/786, 419/768 i.e 1/100608 easily. The following is the detailed procedure to determine the greatest common factor of fractions 532/786, 419/768.

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 532/786,419/768?

Given fractions are 532/786,419/768

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 532/786,419/768, numerators are 532,419

Denominators are 786,768

The GCF of 532,419 is 1 .

LCM of 786,768 is 100608.

The greatest common factor of 532/786,419/768 = [GCF of 532,419]/[LCM of 786,768]= 1/100608

Therefore, the GCF of 532/786,419/768 is 1/100608.

Greatest Common Factor of 532,419

To find the highest common factor of 532,419, we have to find the factors of both numbers and list the highest common factor.

The factors of 532 are 1, 2, 4, 7, 14, 19, 28, 38, 76, 133, 266, 532

The factors of 419 are 1, 419

The HCF of 532,419 is 1.

Lets's calculate GCF of 532,419

Greatest Common Factor (GCF) of 532,419 By Common Division

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

Greatest Common Factor of 532,419 By Matching Biggest Common Factor Method

Now, list down the factors of 532

1,2,4,7,14,19,28,38,76,133,266,532

Now, list down the factors of 419

1,419

Greatest Common Factor

We found the factors 532,419 . The biggest common factor number is the GCF number.
So the greatest common factor 532,419 is 1.

Lets's calculate LCM of 786,768

Lowest Common Multiple of 786,768 using Common Division

2	786, 768
3	393, 384
	131, 128

∴ So the LCM of the given numbers is 2 x 3 x 131 x 128 = 100608

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/100608

Therefore, the GCF of Fractions 532/786,419/768 is 1/100608

Least Common Multiple of 786,768 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 786,768 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(786,768) = 6

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

GCF(786,768) x common factors =6 x 1 = 6

LCM(786,768) = ( 786 × 768 ) / 6

LCM(786,768) = 603648 / 6

LCM(786,768) = 100608

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FAQs on GCF of Fractions of 532/786, 419/768

1. What is the HCF of 532,419?

The HCF of 532,419 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 532/786, 419/768?

Answer: GCF of Numerators as per given numbers 532/786, 419/768 is

GCF of Numerators i.e. for 532,419 is 1

LCM of denominators i.e. for 786,768 is 100608.

Thus, GCF of Fractions is 1/100608.Finally, GCF of Fractions for 532/786, 419/768 is 1/100608.