Highest Common Factor of 816, 68824 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, 68824 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 816, 68824 is 8 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, 68824 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, 68824 is 8.
HCF(816, 68824) = 8
HCF of 816, 68824 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, 68824 is 8.
Highest Common Factor of 816,68824 is 8
Step 1: Since 68824 > 816, we apply the division lemma to 68824 and 816, to get
68824 = 816 x 84 + 280
Step 2: Since the reminder 816 ≠ 0, we apply division lemma to 280 and 816, to get
816 = 280 x 2 + 256
Step 3: We consider the new divisor 280 and the new remainder 256, and apply the division lemma to get
280 = 256 x 1 + 24
We consider the new divisor 256 and the new remainder 24,and apply the division lemma to get
256 = 24 x 10 + 16
We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get
24 = 16 x 1 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 816 and 68824 is 8
Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(256,24) = HCF(280,256) = HCF(816,280) = HCF(68824,816) .
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Frequently Asked Questions on HCF of 816, 68824 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, 68824?
Answer: HCF of 816, 68824 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 816, 68824 using Euclid's Algorithm?
Answer: For arbitrary numbers 816, 68824 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.