GCF of 69/612, 736/729, 598/361
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 69/612, 736/729, 598/361 i.e 23/17895492 easily. The following is the detailed procedure to determine the greatest common factor of fractions 69/612, 736/729, 598/361.
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 69/612,736/729,598/361?
Given fractions are 69/612,736/729,598/361
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 69/612,736/729,598/361, numerators are 69,736,598
Denominators are 612,729,361
The GCF of 69,736,598 is 23 .
LCM of 612,729,361 is 17895492.
The greatest common factor of 69/612,736/729,598/361 = [GCF of 69,736,598]/[LCM of 612,729,361]= 23/17895492
Therefore, the GCF of 69/612,736/729,598/361 is 23/17895492.
To find the highest common factor of 69,736,598, 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 736 are 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736
The factors of 598 are 1, 2, 13, 23, 26, 46, 299, 598
The HCF of 69,736,598 is 23.
Lets's calculate GCF of 69,736,598
| 23 | 69, 736, 598 |
| 3, 32, 26 |
∴ So the GCF of the given numbers is 23 = 23
Greatest Common Factor of 69,736,598 By Matching Biggest Common Factor Method
Now, list down the factors of 69
:1,3,23,69
Now, list down the factors of 736
:1,2,4,8,16,23,32,46,92,184,368,736
Now, list down the factors of 598
:1,2,13,23,26,46,299,598
Greatest Common Factor
We found the factors 69,736,598 . The biggest common factor number is the GCF number.
So the greatest common factor 69,736,598 is 23.
Lets's calculate LCM of 612,729,361
| 3 | 612, 729, 361 |
| 3 | 204, 243, 361 |
| 68, 81, 361 |
∴ So the LCM of the given numbers is 3 x 3 x 68 x 81 x 361 = 17895492
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 23/17895492
Therefore, the GCF of Fractions 69/612,736/729,598/361 is 23/17895492
Least Common Multiple of 612,729,361 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 612,729,361 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(612,729,361) = 1
common factors(in case of two or more numbers have common factors) = 9
GCF(612,729,361) x common factors =1 x 9 = 9
LCM(612,729,361) = ( 612 × 729 × 361 ) / 9
LCM(612,729,361) = 161059428 / 9
LCM(612,729,361) = 17895492
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FAQs on GCF of Fractions of 69/612, 736/729, 598/361
1. What is the HCF of 69,736,598?
The HCF of 69,736,598 is 23
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 69/612, 736/729, 598/361?
Answer: GCF of Numerators as per given numbers 69/612, 736/729, 598/361 is
GCF of Numerators i.e. for 69,736,598 is 23
LCM of denominators i.e. for 612,729,361 is 17895492.
Thus, GCF of Fractions is 23/17895492.Finally, GCF of Fractions for 69/612, 736/729, 598/361 is 23/17895492.