Highest Common Factor of 816, 666, 886 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 816, 666, 886 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 816, 666, 886 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 816, 666, 886 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 816, 666, 886 is 2.
HCF(816, 666, 886) = 2
HCF of 816, 666, 886 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 816, 666, 886 is 2.
Highest Common Factor of 816,666,886 is 2
Step 1: Since 816 > 666, we apply the division lemma to 816 and 666, to get
816 = 666 x 1 + 150
Step 2: Since the reminder 666 ≠ 0, we apply division lemma to 150 and 666, to get
666 = 150 x 4 + 66
Step 3: We consider the new divisor 150 and the new remainder 66, and apply the division lemma to get
150 = 66 x 2 + 18
We consider the new divisor 66 and the new remainder 18,and apply the division lemma to get
66 = 18 x 3 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 816 and 666 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(66,18) = HCF(150,66) = HCF(666,150) = HCF(816,666) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 886 > 6, we apply the division lemma to 886 and 6, to get
886 = 6 x 147 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: 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 6 and 886 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(886,6) .
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Frequently Asked Questions on HCF of 816, 666, 886 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 816, 666, 886?
Answer: HCF of 816, 666, 886 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 816, 666, 886 using Euclid's Algorithm?
Answer: For arbitrary numbers 816, 666, 886 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.