GCF of 360/385, 6705/905
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 360/385, 6705/905 i.e 45/69685 easily. The following is the detailed procedure to determine the greatest common factor of fractions 360/385, 6705/905.
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 360/385,6705/905?
Given fractions are 360/385,6705/905
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 360/385,6705/905, numerators are 360,6705
Denominators are 385,905
The GCF of 360,6705 is 45 .
LCM of 385,905 is 69685.
The greatest common factor of 360/385,6705/905 = [GCF of 360,6705]/[LCM of 385,905]= 45/69685
Therefore, the GCF of 360/385,6705/905 is 45/69685.
To find the highest common factor of 360,6705, we have to find the factors of both numbers and list the highest common factor.
The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
The factors of 6705 are 1, 3, 5, 9, 15, 45, 149, 447, 745, 1341, 2235, 6705
The HCF of 360,6705 is 45.
Lets's calculate GCF of 360,6705
| 3 | 360, 6705 |
| 3 | 120, 2235 |
| 5 | 40, 745 |
| 8, 149 |
∴ So the GCF of the given numbers is 3 x 3 x 5 = 45
Greatest Common Factor of 360,6705 By Matching Biggest Common Factor Method
Now, list down the factors of 360
:1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360
Now, list down the factors of 6705
:1,3,5,9,15,45,149,447,745,1341,2235,6705
Greatest Common Factor
We found the factors 360,6705 . The biggest common factor number is the GCF number.
So the greatest common factor 360,6705 is 45.
Lets's calculate LCM of 385,905
| 5 | 385, 905 |
| 77, 181 |
∴ So the LCM of the given numbers is 5 x 77 x 181 = 69685
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 45/69685
Therefore, the GCF of Fractions 360/385,6705/905 is 45/69685
Least Common Multiple of 385,905 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 385,905 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(385,905) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(385,905) x common factors =5 x 1 = 5
LCM(385,905) = ( 385 × 905 ) / 5
LCM(385,905) = 348425 / 5
LCM(385,905) = 69685
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FAQs on GCF of Fractions of 360/385, 6705/905
1. What is the HCF of 360,6705?
The HCF of 360,6705 is 45
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 360/385, 6705/905?
Answer: GCF of Numerators as per given numbers 360/385, 6705/905 is
GCF of Numerators i.e. for 360,6705 is 45
LCM of denominators i.e. for 385,905 is 69685.
Thus, GCF of Fractions is 45/69685.Finally, GCF of Fractions for 360/385, 6705/905 is 45/69685.