How to Find GCF of 30/140, 87/753, 169/661?

GCF of 30/140, 87/753, 169/661

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 30/140, 87/753, 169/661 i.e 1/69682620 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/140, 87/753, 169/661.

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 30/140,87/753,169/661?

Given fractions are 30/140,87/753,169/661

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 30/140,87/753,169/661, numerators are 30,87,169

Denominators are 140,753,661

The GCF of 30,87,169 is 1 .

LCM of 140,753,661 is 69682620.

The greatest common factor of 30/140,87/753,169/661 = [GCF of 30,87,169]/[LCM of 140,753,661]= 1/69682620

Therefore, the GCF of 30/140,87/753,169/661 is 1/69682620.

Greatest Common Factor of 30,87,169

To find the highest common factor of 30,87,169, we have to find the factors of both numbers and list the highest common factor.

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

The factors of 87 are 1, 3, 29, 87

The factors of 169 are 1, 13, 169

The HCF of 30,87,169 is 1.

Lets's calculate GCF of 30,87,169

Greatest Common Factor (GCF) of 30,87,169 By Common Division

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

Greatest Common Factor of 30,87,169 By Matching Biggest Common Factor Method

Now, list down the factors of 30

1,2,3,5,6,10,15,30

Now, list down the factors of 87

1,3,29,87

Now, list down the factors of 169

1,13,169

Greatest Common Factor

We found the factors 30,87,169 . The biggest common factor number is the GCF number.
So the greatest common factor 30,87,169 is 1.

Lets's calculate LCM of 140,753,661

Lowest Common Multiple of 140,753,661 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 69682620

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/69682620

Therefore, the GCF of Fractions 30/140,87/753,169/661 is 1/69682620

Least Common Multiple of 140,753,661 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 140,753,661 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(140,753,661) = 1

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

GCF(140,753,661) x common factors =1 x 1 = 1

LCM(140,753,661) = ( 140 × 753 × 661 ) / 1

LCM(140,753,661) = 69682620 / 1

LCM(140,753,661) = 69682620

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 30/140, 87/753, 169/661

1. What is the HCF of 30,87,169?

The HCF of 30,87,169 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 30/140, 87/753, 169/661?

Answer: GCF of Numerators as per given numbers 30/140, 87/753, 169/661 is

GCF of Numerators i.e. for 30,87,169 is 1

LCM of denominators i.e. for 140,753,661 is 69682620.

Thus, GCF of Fractions is 1/69682620.Finally, GCF of Fractions for 30/140, 87/753, 169/661 is 1/69682620.