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GCF of 414/612, 9278/689

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 414/612, 9278/689 i.e 2/421668 easily. The following is the detailed procedure to determine the greatest common factor of fractions 414/612, 9278/689.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 414/612,9278/689?

Given fractions are 414/612,9278/689

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 414/612,9278/689, numerators are 414,9278

Denominators are 612,689

The GCF of 414,9278 is 2 .

LCM of 612,689 is 421668.

The greatest common factor of 414/612,9278/689 = [GCF of 414,9278]/[LCM of 612,689]= 2/421668

Therefore, the GCF of 414/612,9278/689 is 2/421668.

Greatest Common Factor of 414,9278

To find the highest common factor of 414,9278, we have to find the factors of both numbers and list the highest common factor.

The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414

The factors of 9278 are 1, 2, 4639, 9278

The HCF of 414,9278 is 2.

Lets's calculate GCF of 414,9278

Greatest Common Factor (GCF) of 414,9278 By Common Division

2 414, 9278
207, 4639

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 414,9278 By Matching Biggest Common Factor Method

Greatest Common Factor of 414,9278 By Matching Biggest Common Factor Method

Now, list down the factors of 414

:

1,2,3,6,9,18,23,46,69,138,207,414

Now, list down the factors of 9278

:

1,2,4639,9278

Greatest Common Factor

We found the factors 414,9278 . The biggest common factor number is the GCF number.
So the greatest common factor 414,9278 is 2.


Lets's calculate LCM of 612,689

Lowest Common Multiple of 612,689 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 421668

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/421668

Therefore, the GCF of Fractions 414/612,9278/689 is 2/421668

Least Common Multiple of 612,689 with GCF Formula

Least Common Multiple of 612,689 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 612,689 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(612,689) = 1

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

GCF(612,689) x common factors =1 x 1 = 1

LCM(612,689) = ( 612 × 689 ) / 1

LCM(612,689) = 421668 / 1

LCM(612,689) = 421668


GCF of Fractions Calculation Examples

FAQs on GCF of Fractions of 414/612, 9278/689

1. What is the HCF of 414,9278?

The HCF of 414,9278 is 2

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 414/612, 9278/689?

Answer: GCF of Numerators as per given numbers 414/612, 9278/689 is

GCF of Numerators i.e. for 414,9278 is 2

LCM of denominators i.e. for 612,689 is 421668.

Thus, GCF of Fractions is 2/421668.Finally, GCF of Fractions for 414/612, 9278/689 is 2/421668.