How to Find GCF of 952/420, 969/978?

GCF of 952/420, 969/978

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 952/420, 969/978 i.e 17/68460 easily. The following is the detailed procedure to determine the greatest common factor of fractions 952/420, 969/978.

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 952/420,969/978?

Given fractions are 952/420,969/978

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 952/420,969/978, numerators are 952,969

Denominators are 420,978

The GCF of 952,969 is 17 .

LCM of 420,978 is 68460.

The greatest common factor of 952/420,969/978 = [GCF of 952,969]/[LCM of 420,978]= 17/68460

Therefore, the GCF of 952/420,969/978 is 17/68460.

Greatest Common Factor of 952,969

To find the highest common factor of 952,969, we have to find the factors of both numbers and list the highest common factor.

The factors of 952 are 1, 2, 4, 7, 8, 14, 17, 28, 34, 56, 68, 119, 136, 238, 476, 952

The factors of 969 are 1, 3, 17, 19, 51, 57, 323, 969

The HCF of 952,969 is 17.

Lets's calculate GCF of 952,969

Greatest Common Factor (GCF) of 952,969 By Common Division

17	952, 969
	56, 57

∴ So the GCF of the given numbers is 17 = 17

Greatest Common Factor of 952,969 By Matching Biggest Common Factor Method

Now, list down the factors of 952

1,2,4,7,8,14,17,28,34,56,68,119,136,238,476,952

Now, list down the factors of 969

1,3,17,19,51,57,323,969

Greatest Common Factor

We found the factors 952,969 . The biggest common factor number is the GCF number.
So the greatest common factor 952,969 is 17.

Lets's calculate LCM of 420,978

Lowest Common Multiple of 420,978 using Common Division

2	420, 978
3	210, 489
	70, 163

∴ So the LCM of the given numbers is 2 x 3 x 70 x 163 = 68460

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/68460

Therefore, the GCF of Fractions 952/420,969/978 is 17/68460

Least Common Multiple of 420,978 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 420,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(420,978) = 6

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

GCF(420,978) x common factors =6 x 1 = 6

LCM(420,978) = ( 420 × 978 ) / 6

LCM(420,978) = 410760 / 6

LCM(420,978) = 68460

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 952/420, 969/978

1. What is the HCF of 952,969?

The HCF of 952,969 is 17

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 952/420, 969/978?

Answer: GCF of Numerators as per given numbers 952/420, 969/978 is

GCF of Numerators i.e. for 952,969 is 17

LCM of denominators i.e. for 420,978 is 68460.

Thus, GCF of Fractions is 17/68460.Finally, GCF of Fractions for 952/420, 969/978 is 17/68460.