GCF of 5870/704, 8424/2174
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5870/704, 8424/2174 i.e 2/765248 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5870/704, 8424/2174.
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 5870/704,8424/2174?
Given fractions are 5870/704,8424/2174
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 5870/704,8424/2174, numerators are 5870,8424
Denominators are 704,2174
The GCF of 5870,8424 is 2 .
LCM of 704,2174 is 765248.
The greatest common factor of 5870/704,8424/2174 = [GCF of 5870,8424]/[LCM of 704,2174]= 2/765248
Therefore, the GCF of 5870/704,8424/2174 is 2/765248.
To find the highest common factor of 5870,8424, we have to find the factors of both numbers and list the highest common factor.
The factors of 5870 are 1, 2, 5, 10, 587, 1174, 2935, 5870
The factors of 8424 are 1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 27, 36, 39, 52, 54, 72, 78, 81, 104, 108, 117, 156, 162, 216, 234, 312, 324, 351, 468, 648, 702, 936, 1053, 1404, 2106, 2808, 4212, 8424
The HCF of 5870,8424 is 2.
Lets's calculate GCF of 5870,8424
| 2 | 5870, 8424 |
| 2935, 4212 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 5870,8424 By Matching Biggest Common Factor Method
Now, list down the factors of 5870
:1,2,5,10,587,1174,2935,5870
Now, list down the factors of 8424
:1,2,3,4,6,8,9,12,13,18,24,26,27,36,39,52,54,72,78,81,104,108,117,156,162,216,234,312,324,351,468,648,702,936,1053,1404,2106,2808,4212,8424
Greatest Common Factor
We found the factors 5870,8424 . The biggest common factor number is the GCF number.
So the greatest common factor 5870,8424 is 2.
Lets's calculate LCM of 704,2174
| 2 | 704, 2174 |
| 352, 1087 |
∴ So the LCM of the given numbers is 2 x 352 x 1087 = 765248
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/765248
Therefore, the GCF of Fractions 5870/704,8424/2174 is 2/765248
Least Common Multiple of 704,2174 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 704,2174 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(704,2174) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(704,2174) x common factors =2 x 1 = 2
LCM(704,2174) = ( 704 × 2174 ) / 2
LCM(704,2174) = 1530496 / 2
LCM(704,2174) = 765248
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FAQs on GCF of Fractions of 5870/704, 8424/2174
1. What is the HCF of 5870,8424?
The HCF of 5870,8424 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 5870/704, 8424/2174?
Answer: GCF of Numerators as per given numbers 5870/704, 8424/2174 is
GCF of Numerators i.e. for 5870,8424 is 2
LCM of denominators i.e. for 704,2174 is 765248.
Thus, GCF of Fractions is 2/765248.Finally, GCF of Fractions for 5870/704, 8424/2174 is 2/765248.