GCF of 865/24, 312/9900
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 865/24, 312/9900 i.e 1/19800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 865/24, 312/9900.
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 865/24,312/9900?
Given fractions are 865/24,312/9900
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 865/24,312/9900, numerators are 865,312
Denominators are 24,9900
The GCF of 865,312 is 1 .
LCM of 24,9900 is 19800.
The greatest common factor of 865/24,312/9900 = [GCF of 865,312]/[LCM of 24,9900]= 1/19800
Therefore, the GCF of 865/24,312/9900 is 1/19800.
To find the highest common factor of 865,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 865 are 1, 5, 173, 865
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 865,312 is 1.
Lets's calculate GCF of 865,312
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 865,312 By Matching Biggest Common Factor Method
Now, list down the factors of 865
:1,5,173,865
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 865,312 . The biggest common factor number is the GCF number.
So the greatest common factor 865,312 is 1.
Lets's calculate LCM of 24,9900
| 2 | 24, 9900 |
| 2 | 12, 4950 |
| 3 | 6, 2475 |
| 2, 825 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 2 x 825 = 19800
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/19800
Therefore, the GCF of Fractions 865/24,312/9900 is 1/19800
Least Common Multiple of 24,9900 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 24,9900 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(24,9900) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(24,9900) x common factors =12 x 1 = 12
LCM(24,9900) = ( 24 × 9900 ) / 12
LCM(24,9900) = 237600 / 12
LCM(24,9900) = 19800
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FAQs on GCF of Fractions of 865/24, 312/9900
1. What is the HCF of 865,312?
The HCF of 865,312 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 865/24, 312/9900?
Answer: GCF of Numerators as per given numbers 865/24, 312/9900 is
GCF of Numerators i.e. for 865,312 is 1
LCM of denominators i.e. for 24,9900 is 19800.
Thus, GCF of Fractions is 1/19800.Finally, GCF of Fractions for 865/24, 312/9900 is 1/19800.