GCF of 705/69, 160/301
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 705/69, 160/301 i.e 5/20769 easily. The following is the detailed procedure to determine the greatest common factor of fractions 705/69, 160/301.
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 705/69,160/301?
Given fractions are 705/69,160/301
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 705/69,160/301, numerators are 705,160
Denominators are 69,301
The GCF of 705,160 is 5 .
LCM of 69,301 is 20769.
The greatest common factor of 705/69,160/301 = [GCF of 705,160]/[LCM of 69,301]= 5/20769
Therefore, the GCF of 705/69,160/301 is 5/20769.
To find the highest common factor of 705,160, we have to find the factors of both numbers and list the highest common factor.
The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705
The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
The HCF of 705,160 is 5.
Lets's calculate GCF of 705,160
| 5 | 705, 160 |
| 141, 32 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 705,160 By Matching Biggest Common Factor Method
Now, list down the factors of 705
:1,3,5,15,47,141,235,705
Now, list down the factors of 160
:1,2,4,5,8,10,16,20,32,40,80,160
Greatest Common Factor
We found the factors 705,160 . The biggest common factor number is the GCF number.
So the greatest common factor 705,160 is 5.
Lets's calculate LCM of 69,301
Given numbers has no common factors except 1. So, there LCM is their product i.e 20769
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/20769
Therefore, the GCF of Fractions 705/69,160/301 is 5/20769
Least Common Multiple of 69,301 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 69,301 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(69,301) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(69,301) x common factors =1 x 1 = 1
LCM(69,301) = ( 69 × 301 ) / 1
LCM(69,301) = 20769 / 1
LCM(69,301) = 20769
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FAQs on GCF of Fractions of 705/69, 160/301
1. What is the HCF of 705,160?
The HCF of 705,160 is 5
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 705/69, 160/301?
Answer: GCF of Numerators as per given numbers 705/69, 160/301 is
GCF of Numerators i.e. for 705,160 is 5
LCM of denominators i.e. for 69,301 is 20769.
Thus, GCF of Fractions is 5/20769.Finally, GCF of Fractions for 705/69, 160/301 is 5/20769.