GCF of 549/14, 169/45, 705/90
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 549/14, 169/45, 705/90 i.e 1/630 easily. The following is the detailed procedure to determine the greatest common factor of fractions 549/14, 169/45, 705/90.
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 549/14,169/45,705/90?
Given fractions are 549/14,169/45,705/90
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 549/14,169/45,705/90, numerators are 549,169,705
Denominators are 14,45,90
The GCF of 549,169,705 is 1 .
LCM of 14,45,90 is 630.
The greatest common factor of 549/14,169/45,705/90 = [GCF of 549,169,705]/[LCM of 14,45,90]= 1/630
Therefore, the GCF of 549/14,169/45,705/90 is 1/630.
To find the highest common factor of 549,169,705, we have to find the factors of both numbers and list the highest common factor.
The factors of 549 are 1, 3, 9, 61, 183, 549
The factors of 169 are 1, 13, 169
The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705
The HCF of 549,169,705 is 1.
Lets's calculate GCF of 549,169,705
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 549,169,705 By Matching Biggest Common Factor Method
Now, list down the factors of 549
:1,3,9,61,183,549
Now, list down the factors of 169
:1,13,169
Now, list down the factors of 705
:1,3,5,15,47,141,235,705
Greatest Common Factor
We found the factors 549,169,705 . The biggest common factor number is the GCF number.
So the greatest common factor 549,169,705 is 1.
Lets's calculate LCM of 14,45,90
| 2 | 14, 45, 90 |
| 3 | 7, 45, 45 |
| 3 | 7, 15, 15 |
| 5 | 7, 5, 5 |
| 7, 1, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 5 x 7 x 1 x 1 = 630
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/630
Therefore, the GCF of Fractions 549/14,169/45,705/90 is 1/630
Least Common Multiple of 14,45,90 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 14,45,90 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,45,90) = 1
common factors(in case of two or more numbers have common factors) = 90
GCF(14,45,90) x common factors =1 x 90 = 90
LCM(14,45,90) = ( 14 × 45 × 90 ) / 90
LCM(14,45,90) = 56700 / 90
LCM(14,45,90) = 630
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FAQs on GCF of Fractions of 549/14, 169/45, 705/90
1. What is the HCF of 549,169,705?
The HCF of 549,169,705 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 549/14, 169/45, 705/90?
Answer: GCF of Numerators as per given numbers 549/14, 169/45, 705/90 is
GCF of Numerators i.e. for 549,169,705 is 1
LCM of denominators i.e. for 14,45,90 is 630.
Thus, GCF of Fractions is 1/630.Finally, GCF of Fractions for 549/14, 169/45, 705/90 is 1/630.