Highest Common Factor of 221, 823 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 221, 823 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 221, 823 is 1 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 221, 823 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 221, 823 is 1.
HCF(221, 823) = 1
HCF of 221, 823 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 221, 823 is 1.
Highest Common Factor of 221,823 is 1
Step 1: Since 823 > 221, we apply the division lemma to 823 and 221, to get
823 = 221 x 3 + 160
Step 2: Since the reminder 221 ≠ 0, we apply division lemma to 160 and 221, to get
221 = 160 x 1 + 61
Step 3: We consider the new divisor 160 and the new remainder 61, and apply the division lemma to get
160 = 61 x 2 + 38
We consider the new divisor 61 and the new remainder 38,and apply the division lemma to get
61 = 38 x 1 + 23
We consider the new divisor 38 and the new remainder 23,and apply the division lemma to get
38 = 23 x 1 + 15
We consider the new divisor 23 and the new remainder 15,and apply the division lemma to get
23 = 15 x 1 + 8
We consider the new divisor 15 and the new remainder 8,and apply the division lemma to get
15 = 8 x 1 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 221 and 823 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(15,8) = HCF(23,15) = HCF(38,23) = HCF(61,38) = HCF(160,61) = HCF(221,160) = HCF(823,221) .
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Frequently Asked Questions on HCF of 221, 823 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 221, 823?
Answer: HCF of 221, 823 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 221, 823 using Euclid's Algorithm?
Answer: For arbitrary numbers 221, 823 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
