GCF of 207/74, 640/106
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 207/74, 640/106 i.e 1/3922 easily. The following is the detailed procedure to determine the greatest common factor of fractions 207/74, 640/106.
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 207/74,640/106?
Given fractions are 207/74,640/106
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 207/74,640/106, numerators are 207,640
Denominators are 74,106
The GCF of 207,640 is 1 .
LCM of 74,106 is 3922.
The greatest common factor of 207/74,640/106 = [GCF of 207,640]/[LCM of 74,106]= 1/3922
Therefore, the GCF of 207/74,640/106 is 1/3922.
To find the highest common factor of 207,640, we have to find the factors of both numbers and list the highest common factor.
The factors of 207 are 1, 3, 9, 23, 69, 207
The factors of 640 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 320, 640
The HCF of 207,640 is 1.
Lets's calculate GCF of 207,640
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 207,640 By Matching Biggest Common Factor Method
Now, list down the factors of 207
:1,3,9,23,69,207
Now, list down the factors of 640
:1,2,4,5,8,10,16,20,32,40,64,80,128,160,320,640
Greatest Common Factor
We found the factors 207,640 . The biggest common factor number is the GCF number.
So the greatest common factor 207,640 is 1.
Lets's calculate LCM of 74,106
| 2 | 74, 106 |
| 37, 53 |
∴ So the LCM of the given numbers is 2 x 37 x 53 = 3922
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3922
Therefore, the GCF of Fractions 207/74,640/106 is 1/3922
Least Common Multiple of 74,106 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 74,106 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,106) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(74,106) x common factors =2 x 1 = 2
LCM(74,106) = ( 74 × 106 ) / 2
LCM(74,106) = 7844 / 2
LCM(74,106) = 3922
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FAQs on GCF of Fractions of 207/74, 640/106
1. What is the HCF of 207,640?
The HCF of 207,640 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 207/74, 640/106?
Answer: GCF of Numerators as per given numbers 207/74, 640/106 is
GCF of Numerators i.e. for 207,640 is 1
LCM of denominators i.e. for 74,106 is 3922.
Thus, GCF of Fractions is 1/3922.Finally, GCF of Fractions for 207/74, 640/106 is 1/3922.