GCF of 870/345, 642/170
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 870/345, 642/170 i.e 6/11730 easily. The following is the detailed procedure to determine the greatest common factor of fractions 870/345, 642/170.
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 870/345,642/170?
Given fractions are 870/345,642/170
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 870/345,642/170, numerators are 870,642
Denominators are 345,170
The GCF of 870,642 is 6 .
LCM of 345,170 is 11730.
The greatest common factor of 870/345,642/170 = [GCF of 870,642]/[LCM of 345,170]= 6/11730
Therefore, the GCF of 870/345,642/170 is 6/11730.
To find the highest common factor of 870,642, we have to find the factors of both numbers and list the highest common factor.
The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870
The factors of 642 are 1, 2, 3, 6, 107, 214, 321, 642
The HCF of 870,642 is 6.
Lets's calculate GCF of 870,642
| 2 | 870, 642 |
| 3 | 435, 321 |
| 145, 107 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 870,642 By Matching Biggest Common Factor Method
Now, list down the factors of 870
:1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870
Now, list down the factors of 642
:1,2,3,6,107,214,321,642
Greatest Common Factor
We found the factors 870,642 . The biggest common factor number is the GCF number.
So the greatest common factor 870,642 is 6.
Lets's calculate LCM of 345,170
| 5 | 345, 170 |
| 69, 34 |
∴ So the LCM of the given numbers is 5 x 69 x 34 = 11730
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/11730
Therefore, the GCF of Fractions 870/345,642/170 is 6/11730
Least Common Multiple of 345,170 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 345,170 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(345,170) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(345,170) x common factors =5 x 1 = 5
LCM(345,170) = ( 345 × 170 ) / 5
LCM(345,170) = 58650 / 5
LCM(345,170) = 11730
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FAQs on GCF of Fractions of 870/345, 642/170
1. What is the HCF of 870,642?
The HCF of 870,642 is 6
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 870/345, 642/170?
Answer: GCF of Numerators as per given numbers 870/345, 642/170 is
GCF of Numerators i.e. for 870,642 is 6
LCM of denominators i.e. for 345,170 is 11730.
Thus, GCF of Fractions is 6/11730.Finally, GCF of Fractions for 870/345, 642/170 is 6/11730.