GCF of 8202/219, 9632/7703
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8202/219, 9632/7703 i.e 2/1686957 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8202/219, 9632/7703.
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 8202/219,9632/7703?
Given fractions are 8202/219,9632/7703
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 8202/219,9632/7703, numerators are 8202,9632
Denominators are 219,7703
The GCF of 8202,9632 is 2 .
LCM of 219,7703 is 1686957.
The greatest common factor of 8202/219,9632/7703 = [GCF of 8202,9632]/[LCM of 219,7703]= 2/1686957
Therefore, the GCF of 8202/219,9632/7703 is 2/1686957.
To find the highest common factor of 8202,9632, we have to find the factors of both numbers and list the highest common factor.
The factors of 8202 are 1, 2, 3, 6, 1367, 2734, 4101, 8202
The factors of 9632 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 43, 56, 86, 112, 172, 224, 301, 344, 602, 688, 1204, 1376, 2408, 4816, 9632
The HCF of 8202,9632 is 2.
Lets's calculate GCF of 8202,9632
| 2 | 8202, 9632 |
| 4101, 4816 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 8202,9632 By Matching Biggest Common Factor Method
Now, list down the factors of 8202
:1,2,3,6,1367,2734,4101,8202
Now, list down the factors of 9632
:1,2,4,7,8,14,16,28,32,43,56,86,112,172,224,301,344,602,688,1204,1376,2408,4816,9632
Greatest Common Factor
We found the factors 8202,9632 . The biggest common factor number is the GCF number.
So the greatest common factor 8202,9632 is 2.
Lets's calculate LCM of 219,7703
Given numbers has no common factors except 1. So, there LCM is their product i.e 1686957
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1686957
Therefore, the GCF of Fractions 8202/219,9632/7703 is 2/1686957
Least Common Multiple of 219,7703 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 219,7703 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(219,7703) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(219,7703) x common factors =1 x 1 = 1
LCM(219,7703) = ( 219 × 7703 ) / 1
LCM(219,7703) = 1686957 / 1
LCM(219,7703) = 1686957
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FAQs on GCF of Fractions of 8202/219, 9632/7703
1. What is the HCF of 8202,9632?
The HCF of 8202,9632 is 2
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 8202/219, 9632/7703?
Answer: GCF of Numerators as per given numbers 8202/219, 9632/7703 is
GCF of Numerators i.e. for 8202,9632 is 2
LCM of denominators i.e. for 219,7703 is 1686957.
Thus, GCF of Fractions is 2/1686957.Finally, GCF of Fractions for 8202/219, 9632/7703 is 2/1686957.