How to Find GCF of 69/285, 78/974, 837/954?

GCF of 69/285, 78/974, 837/954

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 69/285, 78/974, 837/954 i.e 3/44136810 easily. The following is the detailed procedure to determine the greatest common factor of fractions 69/285, 78/974, 837/954.

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 69/285,78/974,837/954?

Given fractions are 69/285,78/974,837/954

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 69/285,78/974,837/954, numerators are 69,78,837

Denominators are 285,974,954

The GCF of 69,78,837 is 3 .

LCM of 285,974,954 is 44136810.

The greatest common factor of 69/285,78/974,837/954 = [GCF of 69,78,837]/[LCM of 285,974,954]= 3/44136810

Therefore, the GCF of 69/285,78/974,837/954 is 3/44136810.

Greatest Common Factor of 69,78,837

To find the highest common factor of 69,78,837, we have to find the factors of both numbers and list the highest common factor.

The factors of 69 are 1, 3, 23, 69

The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78

The factors of 837 are 1, 3, 9, 27, 31, 93, 279, 837

The HCF of 69,78,837 is 3.

Lets's calculate GCF of 69,78,837

Greatest Common Factor (GCF) of 69,78,837 By Common Division

3	69, 78, 837
	23, 26, 279

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 69,78,837 By Matching Biggest Common Factor Method

Now, list down the factors of 69

1,3,23,69

Now, list down the factors of 78

1,2,3,6,13,26,39,78

Now, list down the factors of 837

1,3,9,27,31,93,279,837

Greatest Common Factor

We found the factors 69,78,837 . The biggest common factor number is the GCF number.
So the greatest common factor 69,78,837 is 3.

Lets's calculate LCM of 285,974,954

Lowest Common Multiple of 285,974,954 using Common Division

2	285, 974, 954
3	285, 487, 477
	95, 487, 159

∴ So the LCM of the given numbers is 2 x 3 x 95 x 487 x 159 = 44136810

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/44136810

Therefore, the GCF of Fractions 69/285,78/974,837/954 is 3/44136810

Least Common Multiple of 285,974,954 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 285,974,954 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(285,974,954) = 1

common factors(in case of two or more numbers have common factors) = 6

GCF(285,974,954) x common factors =1 x 6 = 6

LCM(285,974,954) = ( 285 × 974 × 954 ) / 6

LCM(285,974,954) = 264820860 / 6

LCM(285,974,954) = 44136810

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 69/285, 78/974, 837/954

1. What is the HCF of 69,78,837?

The HCF of 69,78,837 is 3

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 69/285, 78/974, 837/954?

Answer: GCF of Numerators as per given numbers 69/285, 78/974, 837/954 is

GCF of Numerators i.e. for 69,78,837 is 3

LCM of denominators i.e. for 285,974,954 is 44136810.

Thus, GCF of Fractions is 3/44136810.Finally, GCF of Fractions for 69/285, 78/974, 837/954 is 3/44136810.