GCF of 75/172, 775/345, 677/106
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 75/172, 775/345, 677/106 i.e 1/3145020 easily. The following is the detailed procedure to determine the greatest common factor of fractions 75/172, 775/345, 677/106.
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 75/172,775/345,677/106?
Given fractions are 75/172,775/345,677/106
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 75/172,775/345,677/106, numerators are 75,775,677
Denominators are 172,345,106
The GCF of 75,775,677 is 1 .
LCM of 172,345,106 is 3145020.
The greatest common factor of 75/172,775/345,677/106 = [GCF of 75,775,677]/[LCM of 172,345,106]= 1/3145020
Therefore, the GCF of 75/172,775/345,677/106 is 1/3145020.
To find the highest common factor of 75,775,677, we have to find the factors of both numbers and list the highest common factor.
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 775 are 1, 5, 25, 31, 155, 775
The factors of 677 are 1, 677
The HCF of 75,775,677 is 1.
Lets's calculate GCF of 75,775,677
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 75,775,677 By Matching Biggest Common Factor Method
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 775
:1,5,25,31,155,775
Now, list down the factors of 677
:1,677
Greatest Common Factor
We found the factors 75,775,677 . The biggest common factor number is the GCF number.
So the greatest common factor 75,775,677 is 1.
Lets's calculate LCM of 172,345,106
| 2 | 172, 345, 106 |
| 86, 345, 53 |
∴ So the LCM of the given numbers is 2 x 86 x 345 x 53 = 3145020
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3145020
Therefore, the GCF of Fractions 75/172,775/345,677/106 is 1/3145020
Least Common Multiple of 172,345,106 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 172,345,106 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(172,345,106) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(172,345,106) x common factors =1 x 2 = 2
LCM(172,345,106) = ( 172 × 345 × 106 ) / 2
LCM(172,345,106) = 6290040 / 2
LCM(172,345,106) = 3145020
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FAQs on GCF of Fractions of 75/172, 775/345, 677/106
1. What is the HCF of 75,775,677?
The HCF of 75,775,677 is 1
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 75/172, 775/345, 677/106?
Answer: GCF of Numerators as per given numbers 75/172, 775/345, 677/106 is
GCF of Numerators i.e. for 75,775,677 is 1
LCM of denominators i.e. for 172,345,106 is 3145020.
Thus, GCF of Fractions is 1/3145020.Finally, GCF of Fractions for 75/172, 775/345, 677/106 is 1/3145020.