Highest Common Factor of 823, 460 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 823, 460 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 823, 460 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 823, 460 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 823, 460 is 1.
HCF(823, 460) = 1
HCF of 823, 460 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 823, 460 is 1.
Highest Common Factor of 823,460 is 1
Step 1: Since 823 > 460, we apply the division lemma to 823 and 460, to get
823 = 460 x 1 + 363
Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 363 and 460, to get
460 = 363 x 1 + 97
Step 3: We consider the new divisor 363 and the new remainder 97, and apply the division lemma to get
363 = 97 x 3 + 72
We consider the new divisor 97 and the new remainder 72,and apply the division lemma to get
97 = 72 x 1 + 25
We consider the new divisor 72 and the new remainder 25,and apply the division lemma to get
72 = 25 x 2 + 22
We consider the new divisor 25 and the new remainder 22,and apply the division lemma to get
25 = 22 x 1 + 3
We consider the new divisor 22 and the new remainder 3,and apply the division lemma to get
22 = 3 x 7 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 823 and 460 is 1
Notice that 1 = HCF(3,1) = HCF(22,3) = HCF(25,22) = HCF(72,25) = HCF(97,72) = HCF(363,97) = HCF(460,363) = HCF(823,460) .
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Frequently Asked Questions on HCF of 823, 460 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 823, 460?
Answer: HCF of 823, 460 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 823, 460 using Euclid's Algorithm?
Answer: For arbitrary numbers 823, 460 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.