GCF of 609/480, 714/657
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 609/480, 714/657 i.e 21/105120 easily. The following is the detailed procedure to determine the greatest common factor of fractions 609/480, 714/657.
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 609/480,714/657?
Given fractions are 609/480,714/657
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 609/480,714/657, numerators are 609,714
Denominators are 480,657
The GCF of 609,714 is 21 .
LCM of 480,657 is 105120.
The greatest common factor of 609/480,714/657 = [GCF of 609,714]/[LCM of 480,657]= 21/105120
Therefore, the GCF of 609/480,714/657 is 21/105120.
To find the highest common factor of 609,714, we have to find the factors of both numbers and list the highest common factor.
The factors of 609 are 1, 3, 7, 21, 29, 87, 203, 609
The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714
The HCF of 609,714 is 21.
Lets's calculate GCF of 609,714
| 3 | 609, 714 |
| 7 | 203, 238 |
| 29, 34 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 609,714 By Matching Biggest Common Factor Method
Now, list down the factors of 609
:1,3,7,21,29,87,203,609
Now, list down the factors of 714
:1,2,3,6,7,14,17,21,34,42,51,102,119,238,357,714
Greatest Common Factor
We found the factors 609,714 . The biggest common factor number is the GCF number.
So the greatest common factor 609,714 is 21.
Lets's calculate LCM of 480,657
| 3 | 480, 657 |
| 160, 219 |
∴ So the LCM of the given numbers is 3 x 160 x 219 = 105120
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/105120
Therefore, the GCF of Fractions 609/480,714/657 is 21/105120
Least Common Multiple of 480,657 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 480,657 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(480,657) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(480,657) x common factors =3 x 1 = 3
LCM(480,657) = ( 480 × 657 ) / 3
LCM(480,657) = 315360 / 3
LCM(480,657) = 105120
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FAQs on GCF of Fractions of 609/480, 714/657
1. What is the HCF of 609,714?
The HCF of 609,714 is 21
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 609/480, 714/657?
Answer: GCF of Numerators as per given numbers 609/480, 714/657 is
GCF of Numerators i.e. for 609,714 is 21
LCM of denominators i.e. for 480,657 is 105120.
Thus, GCF of Fractions is 21/105120.Finally, GCF of Fractions for 609/480, 714/657 is 21/105120.