How to Find GCF of 69/16, 70/314, 802/348?

GCF of 69/16, 70/314, 802/348

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 69/16, 70/314, 802/348 i.e 1/218544 easily. The following is the detailed procedure to determine the greatest common factor of fractions 69/16, 70/314, 802/348.

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 69/16,70/314,802/348?

Given fractions are 69/16,70/314,802/348

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 69/16,70/314,802/348, numerators are 69,70,802

Denominators are 16,314,348

The GCF of 69,70,802 is 1 .

LCM of 16,314,348 is 218544.

The greatest common factor of 69/16,70/314,802/348 = [GCF of 69,70,802]/[LCM of 16,314,348]= 1/218544

Therefore, the GCF of 69/16,70/314,802/348 is 1/218544.

Greatest Common Factor of 69,70,802

To find the highest common factor of 69,70,802, 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 70 are 1, 2, 5, 7, 10, 14, 35, 70

The factors of 802 are 1, 2, 401, 802

The HCF of 69,70,802 is 1.

Lets's calculate GCF of 69,70,802

Greatest Common Factor (GCF) of 69,70,802 By Common Division

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

Greatest Common Factor of 69,70,802 By Matching Biggest Common Factor Method

Now, list down the factors of 69

1,3,23,69

Now, list down the factors of 70

1,2,5,7,10,14,35,70

Now, list down the factors of 802

1,2,401,802

Greatest Common Factor

We found the factors 69,70,802 . The biggest common factor number is the GCF number.
So the greatest common factor 69,70,802 is 1.

Lets's calculate LCM of 16,314,348

Lowest Common Multiple of 16,314,348 using Common Division

2	16, 314, 348
2	8, 157, 174
	4, 157, 87

∴ So the LCM of the given numbers is 2 x 2 x 4 x 157 x 87 = 218544

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/218544

Therefore, the GCF of Fractions 69/16,70/314,802/348 is 1/218544

Least Common Multiple of 16,314,348 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 16,314,348 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(16,314,348) = 2

common factors(in case of two or more numbers have common factors) = 4

GCF(16,314,348) x common factors =2 x 4 = 8

LCM(16,314,348) = ( 16 × 314 × 348 ) / 8

LCM(16,314,348) = 1748352 / 8

LCM(16,314,348) = 218544

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 69/16, 70/314, 802/348

1. What is the HCF of 69,70,802?

The HCF of 69,70,802 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 69/16, 70/314, 802/348?

Answer: GCF of Numerators as per given numbers 69/16, 70/314, 802/348 is

GCF of Numerators i.e. for 69,70,802 is 1

LCM of denominators i.e. for 16,314,348 is 218544.

Thus, GCF of Fractions is 1/218544.Finally, GCF of Fractions for 69/16, 70/314, 802/348 is 1/218544.