GCF of 735/28, 189/149
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 735/28, 189/149 i.e 21/4172 easily. The following is the detailed procedure to determine the greatest common factor of fractions 735/28, 189/149.
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 735/28,189/149?
Given fractions are 735/28,189/149
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 735/28,189/149, numerators are 735,189
Denominators are 28,149
The GCF of 735,189 is 21 .
LCM of 28,149 is 4172.
The greatest common factor of 735/28,189/149 = [GCF of 735,189]/[LCM of 28,149]= 21/4172
Therefore, the GCF of 735/28,189/149 is 21/4172.
To find the highest common factor of 735,189, we have to find the factors of both numbers and list the highest common factor.
The factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189
The HCF of 735,189 is 21.
Lets's calculate GCF of 735,189
| 3 | 735, 189 |
| 7 | 245, 63 |
| 35, 9 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 735,189 By Matching Biggest Common Factor Method
Now, list down the factors of 735
:1,3,5,7,15,21,35,49,105,147,245,735
Now, list down the factors of 189
:1,3,7,9,21,27,63,189
Greatest Common Factor
We found the factors 735,189 . The biggest common factor number is the GCF number.
So the greatest common factor 735,189 is 21.
Lets's calculate LCM of 28,149
Given numbers has no common factors except 1. So, there LCM is their product i.e 4172
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/4172
Therefore, the GCF of Fractions 735/28,189/149 is 21/4172
Least Common Multiple of 28,149 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 28,149 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(28,149) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(28,149) x common factors =1 x 1 = 1
LCM(28,149) = ( 28 × 149 ) / 1
LCM(28,149) = 4172 / 1
LCM(28,149) = 4172
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FAQs on GCF of Fractions of 735/28, 189/149
1. What is the HCF of 735,189?
The HCF of 735,189 is 21
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 735/28, 189/149?
Answer: GCF of Numerators as per given numbers 735/28, 189/149 is
GCF of Numerators i.e. for 735,189 is 21
LCM of denominators i.e. for 28,149 is 4172.
Thus, GCF of Fractions is 21/4172.Finally, GCF of Fractions for 735/28, 189/149 is 21/4172.