GCF of 8214/830, 4207/719
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8214/830, 4207/719 i.e 1/596770 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8214/830, 4207/719.
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 8214/830,4207/719?
Given fractions are 8214/830,4207/719
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 8214/830,4207/719, numerators are 8214,4207
Denominators are 830,719
The GCF of 8214,4207 is 1 .
LCM of 830,719 is 596770.
The greatest common factor of 8214/830,4207/719 = [GCF of 8214,4207]/[LCM of 830,719]= 1/596770
Therefore, the GCF of 8214/830,4207/719 is 1/596770.
To find the highest common factor of 8214,4207, we have to find the factors of both numbers and list the highest common factor.
The factors of 8214 are 1, 2, 3, 6, 37, 74, 111, 222, 1369, 2738, 4107, 8214
The factors of 4207 are 1, 7, 601, 4207
The HCF of 8214,4207 is 1.
Lets's calculate GCF of 8214,4207
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 8214,4207 By Matching Biggest Common Factor Method
Now, list down the factors of 8214
:1,2,3,6,37,74,111,222,1369,2738,4107,8214
Now, list down the factors of 4207
:1,7,601,4207
Greatest Common Factor
We found the factors 8214,4207 . The biggest common factor number is the GCF number.
So the greatest common factor 8214,4207 is 1.
Lets's calculate LCM of 830,719
Given numbers has no common factors except 1. So, there LCM is their product i.e 596770
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/596770
Therefore, the GCF of Fractions 8214/830,4207/719 is 1/596770
Least Common Multiple of 830,719 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 830,719 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(830,719) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(830,719) x common factors =1 x 1 = 1
LCM(830,719) = ( 830 × 719 ) / 1
LCM(830,719) = 596770 / 1
LCM(830,719) = 596770
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FAQs on GCF of Fractions of 8214/830, 4207/719
1. What is the HCF of 8214,4207?
The HCF of 8214,4207 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 8214/830, 4207/719?
Answer: GCF of Numerators as per given numbers 8214/830, 4207/719 is
GCF of Numerators i.e. for 8214,4207 is 1
LCM of denominators i.e. for 830,719 is 596770.
Thus, GCF of Fractions is 1/596770.Finally, GCF of Fractions for 8214/830, 4207/719 is 1/596770.