How to Find GCF of 64/456, 1689/9538?

GCF of 64/456, 1689/9538

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 64/456, 1689/9538 i.e 1/114456 easily. The following is the detailed procedure to determine the greatest common factor of fractions 64/456, 1689/9538.

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 64/456,1689/9538?

Given fractions are 64/456,1689/9538

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 64/456,1689/9538, numerators are 64,1689

Denominators are 456,9538

The GCF of 64,1689 is 1 .

LCM of 456,9538 is 114456.

The greatest common factor of 64/456,1689/9538 = [GCF of 64,1689]/[LCM of 456,9538]= 1/114456

Therefore, the GCF of 64/456,1689/9538 is 1/114456.

Greatest Common Factor of 64,1689

To find the highest common factor of 64,1689, we have to find the factors of both numbers and list the highest common factor.

The factors of 64 are 1, 2, 4, 8, 16, 32, 64

The factors of 1689 are 1, 3, 563, 1689

The HCF of 64,1689 is 1.

Lets's calculate GCF of 64,1689

Greatest Common Factor (GCF) of 64,1689 By Common Division

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

Greatest Common Factor of 64,1689 By Matching Biggest Common Factor Method

Now, list down the factors of 64

1,2,4,8,16,32,64

Now, list down the factors of 1689

1,3,563,1689

Greatest Common Factor

We found the factors 64,1689 . The biggest common factor number is the GCF number.
So the greatest common factor 64,1689 is 1.

Lets's calculate LCM of 456,9538

Lowest Common Multiple of 456,9538 using Common Division

2	456, 9538
19	228, 4769
	12, 251

∴ So the LCM of the given numbers is 2 x 19 x 12 x 251 = 114456

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/114456

Therefore, the GCF of Fractions 64/456,1689/9538 is 1/114456

Least Common Multiple of 456,9538 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 456,9538 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(456,9538) = 38

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

GCF(456,9538) x common factors =38 x 1 = 38

LCM(456,9538) = ( 456 × 9538 ) / 38

LCM(456,9538) = 4349328 / 38

LCM(456,9538) = 114456

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FAQs on GCF of Fractions of 64/456, 1689/9538

1. What is the HCF of 64,1689?

The HCF of 64,1689 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 64/456, 1689/9538?

Answer: GCF of Numerators as per given numbers 64/456, 1689/9538 is

GCF of Numerators i.e. for 64,1689 is 1

LCM of denominators i.e. for 456,9538 is 114456.

Thus, GCF of Fractions is 1/114456.Finally, GCF of Fractions for 64/456, 1689/9538 is 1/114456.