Highest Common Factor of 822, 864 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, 864 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 822, 864 is 6 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, 864 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, 864 is 6.
HCF(822, 864) = 6
HCF of 822, 864 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, 864 is 6.
Highest Common Factor of 822,864 is 6
Step 1: Since 864 > 822, we apply the division lemma to 864 and 822, to get
864 = 822 x 1 + 42
Step 2: Since the reminder 822 ≠ 0, we apply division lemma to 42 and 822, to get
822 = 42 x 19 + 24
Step 3: We consider the new divisor 42 and the new remainder 24, and apply the division lemma to get
42 = 24 x 1 + 18
We consider the new divisor 24 and the new remainder 18,and apply the division lemma to get
24 = 18 x 1 + 6
We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 822 and 864 is 6
Notice that 6 = HCF(18,6) = HCF(24,18) = HCF(42,24) = HCF(822,42) = HCF(864,822) .
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Frequently Asked Questions on HCF of 822, 864 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, 864?
Answer: HCF of 822, 864 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 822, 864 using Euclid's Algorithm?
Answer: For arbitrary numbers 822, 864 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.