Highest Common Factor of 822, 8516 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 822, 8516 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 822, 8516 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 822, 8516 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 822, 8516 is 2.
HCF(822, 8516) = 2
HCF of 822, 8516 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 822, 8516 is 2.
Highest Common Factor of 822,8516 is 2
Step 1: Since 8516 > 822, we apply the division lemma to 8516 and 822, to get
8516 = 822 x 10 + 296
Step 2: Since the reminder 822 ≠ 0, we apply division lemma to 296 and 822, to get
822 = 296 x 2 + 230
Step 3: We consider the new divisor 296 and the new remainder 230, and apply the division lemma to get
296 = 230 x 1 + 66
We consider the new divisor 230 and the new remainder 66,and apply the division lemma to get
230 = 66 x 3 + 32
We consider the new divisor 66 and the new remainder 32,and apply the division lemma to get
66 = 32 x 2 + 2
We consider the new divisor 32 and the new remainder 2,and apply the division lemma to get
32 = 2 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 822 and 8516 is 2
Notice that 2 = HCF(32,2) = HCF(66,32) = HCF(230,66) = HCF(296,230) = HCF(822,296) = HCF(8516,822) .
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Frequently Asked Questions on HCF of 822, 8516 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 822, 8516?
Answer: HCF of 822, 8516 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 822, 8516 using Euclid's Algorithm?
Answer: For arbitrary numbers 822, 8516 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.