Highest Common Factor of 774, 866, 314 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 774, 866, 314 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 774, 866, 314 is 2 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 774, 866, 314 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 774, 866, 314 is 2.
HCF(774, 866, 314) = 2
HCF of 774, 866, 314 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 774, 866, 314 is 2.
Highest Common Factor of 774,866,314 is 2
Step 1: Since 866 > 774, we apply the division lemma to 866 and 774, to get
866 = 774 x 1 + 92
Step 2: Since the reminder 774 ≠ 0, we apply division lemma to 92 and 774, to get
774 = 92 x 8 + 38
Step 3: We consider the new divisor 92 and the new remainder 38, and apply the division lemma to get
92 = 38 x 2 + 16
We consider the new divisor 38 and the new remainder 16,and apply the division lemma to get
38 = 16 x 2 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 774 and 866 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(38,16) = HCF(92,38) = HCF(774,92) = HCF(866,774) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 314 > 2, we apply the division lemma to 314 and 2, to get
314 = 2 x 157 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 314 is 2
Notice that 2 = HCF(314,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 774, 866, 314 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 774, 866, 314?
Answer: HCF of 774, 866, 314 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 774, 866, 314 using Euclid's Algorithm?
Answer: For arbitrary numbers 774, 866, 314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.