GCF of 8460/154, 9738/1308
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8460/154, 9738/1308 i.e 18/100716 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8460/154, 9738/1308.
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 8460/154,9738/1308?
Given fractions are 8460/154,9738/1308
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 8460/154,9738/1308, numerators are 8460,9738
Denominators are 154,1308
The GCF of 8460,9738 is 18 .
LCM of 154,1308 is 100716.
The greatest common factor of 8460/154,9738/1308 = [GCF of 8460,9738]/[LCM of 154,1308]= 18/100716
Therefore, the GCF of 8460/154,9738/1308 is 18/100716.
To find the highest common factor of 8460,9738, we have to find the factors of both numbers and list the highest common factor.
The factors of 8460 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 47, 60, 90, 94, 141, 180, 188, 235, 282, 423, 470, 564, 705, 846, 940, 1410, 1692, 2115, 2820, 4230, 8460
The factors of 9738 are 1, 2, 3, 6, 9, 18, 541, 1082, 1623, 3246, 4869, 9738
The HCF of 8460,9738 is 18.
Lets's calculate GCF of 8460,9738
| 2 | 8460, 9738 |
| 3 | 4230, 4869 |
| 3 | 1410, 1623 |
| 470, 541 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 8460,9738 By Matching Biggest Common Factor Method
Now, list down the factors of 8460
:1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,47,60,90,94,141,180,188,235,282,423,470,564,705,846,940,1410,1692,2115,2820,4230,8460
Now, list down the factors of 9738
:1,2,3,6,9,18,541,1082,1623,3246,4869,9738
Greatest Common Factor
We found the factors 8460,9738 . The biggest common factor number is the GCF number.
So the greatest common factor 8460,9738 is 18.
Lets's calculate LCM of 154,1308
| 2 | 154, 1308 |
| 77, 654 |
∴ So the LCM of the given numbers is 2 x 77 x 654 = 100716
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/100716
Therefore, the GCF of Fractions 8460/154,9738/1308 is 18/100716
Least Common Multiple of 154,1308 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 154,1308 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(154,1308) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(154,1308) x common factors =2 x 1 = 2
LCM(154,1308) = ( 154 × 1308 ) / 2
LCM(154,1308) = 201432 / 2
LCM(154,1308) = 100716
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FAQs on GCF of Fractions of 8460/154, 9738/1308
1. What is the HCF of 8460,9738?
The HCF of 8460,9738 is 18
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 8460/154, 9738/1308?
Answer: GCF of Numerators as per given numbers 8460/154, 9738/1308 is
GCF of Numerators i.e. for 8460,9738 is 18
LCM of denominators i.e. for 154,1308 is 100716.
Thus, GCF of Fractions is 18/100716.Finally, GCF of Fractions for 8460/154, 9738/1308 is 18/100716.