How to Find GCF of 174/21, 630/457?

GCF of 174/21, 630/457

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 174/21, 630/457 i.e 6/9597 easily. The following is the detailed procedure to determine the greatest common factor of fractions 174/21, 630/457.

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 174/21,630/457?

Given fractions are 174/21,630/457

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 174/21,630/457, numerators are 174,630

Denominators are 21,457

The GCF of 174,630 is 6 .

LCM of 21,457 is 9597.

The greatest common factor of 174/21,630/457 = [GCF of 174,630]/[LCM of 21,457]= 6/9597

Therefore, the GCF of 174/21,630/457 is 6/9597.

Greatest Common Factor of 174,630

To find the highest common factor of 174,630, we have to find the factors of both numbers and list the highest common factor.

The factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174

The factors of 630 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630

The HCF of 174,630 is 6.

Lets's calculate GCF of 174,630

Greatest Common Factor (GCF) of 174,630 By Common Division

2	174, 630
3	87, 315
	29, 105

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 174,630 By Matching Biggest Common Factor Method

Now, list down the factors of 174

1,2,3,6,29,58,87,174

Now, list down the factors of 630

1,2,3,5,6,7,9,10,14,15,18,21,30,35,42,45,63,70,90,105,126,210,315,630

Greatest Common Factor

We found the factors 174,630 . The biggest common factor number is the GCF number.
So the greatest common factor 174,630 is 6.

Lets's calculate LCM of 21,457

Lowest Common Multiple of 21,457 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 9597

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/9597

Therefore, the GCF of Fractions 174/21,630/457 is 6/9597

Least Common Multiple of 21,457 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 21,457 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(21,457) = 1

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

GCF(21,457) x common factors =1 x 1 = 1

LCM(21,457) = ( 21 × 457 ) / 1

LCM(21,457) = 9597 / 1

LCM(21,457) = 9597

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FAQs on GCF of Fractions of 174/21, 630/457

1. What is the HCF of 174,630?

The HCF of 174,630 is 6

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 174/21, 630/457?

Answer: GCF of Numerators as per given numbers 174/21, 630/457 is

GCF of Numerators i.e. for 174,630 is 6

LCM of denominators i.e. for 21,457 is 9597.

Thus, GCF of Fractions is 6/9597.Finally, GCF of Fractions for 174/21, 630/457 is 6/9597.