GCF of 688/49, 952/90, 709/60
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 688/49, 952/90, 709/60 i.e 1/8820 easily. The following is the detailed procedure to determine the greatest common factor of fractions 688/49, 952/90, 709/60.
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 688/49,952/90,709/60?
Given fractions are 688/49,952/90,709/60
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 688/49,952/90,709/60, numerators are 688,952,709
Denominators are 49,90,60
The GCF of 688,952,709 is 1 .
LCM of 49,90,60 is 8820.
The greatest common factor of 688/49,952/90,709/60 = [GCF of 688,952,709]/[LCM of 49,90,60]= 1/8820
Therefore, the GCF of 688/49,952/90,709/60 is 1/8820.
To find the highest common factor of 688,952,709, we have to find the factors of both numbers and list the highest common factor.
The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The factors of 952 are 1, 2, 4, 7, 8, 14, 17, 28, 34, 56, 68, 119, 136, 238, 476, 952
The factors of 709 are 1, 709
The HCF of 688,952,709 is 1.
Lets's calculate GCF of 688,952,709
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 688,952,709 By Matching Biggest Common Factor Method
Now, list down the factors of 688
:1,2,4,8,16,43,86,172,344,688
Now, list down the factors of 952
:1,2,4,7,8,14,17,28,34,56,68,119,136,238,476,952
Now, list down the factors of 709
:1,709
Greatest Common Factor
We found the factors 688,952,709 . The biggest common factor number is the GCF number.
So the greatest common factor 688,952,709 is 1.
Lets's calculate LCM of 49,90,60
| 2 | 49, 90, 60 |
| 3 | 49, 45, 30 |
| 5 | 49, 15, 10 |
| 49, 3, 2 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 49 x 3 x 2 = 8820
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8820
Therefore, the GCF of Fractions 688/49,952/90,709/60 is 1/8820
Least Common Multiple of 49,90,60 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 49,90,60 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(49,90,60) = 1
common factors(in case of two or more numbers have common factors) = 30
GCF(49,90,60) x common factors =1 x 30 = 30
LCM(49,90,60) = ( 49 × 90 × 60 ) / 30
LCM(49,90,60) = 264600 / 30
LCM(49,90,60) = 8820
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 688/49, 952/90, 709/60
1. What is the HCF of 688,952,709?
The HCF of 688,952,709 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 688/49, 952/90, 709/60?
Answer: GCF of Numerators as per given numbers 688/49, 952/90, 709/60 is
GCF of Numerators i.e. for 688,952,709 is 1
LCM of denominators i.e. for 49,90,60 is 8820.
Thus, GCF of Fractions is 1/8820.Finally, GCF of Fractions for 688/49, 952/90, 709/60 is 1/8820.