Highest Common Factor of 823, 8073 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, 8073 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 823, 8073 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, 8073 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, 8073 is 1.
HCF(823, 8073) = 1
HCF of 823, 8073 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, 8073 is 1.
Highest Common Factor of 823,8073 is 1
Step 1: Since 8073 > 823, we apply the division lemma to 8073 and 823, to get
8073 = 823 x 9 + 666
Step 2: Since the reminder 823 ≠ 0, we apply division lemma to 666 and 823, to get
823 = 666 x 1 + 157
Step 3: We consider the new divisor 666 and the new remainder 157, and apply the division lemma to get
666 = 157 x 4 + 38
We consider the new divisor 157 and the new remainder 38,and apply the division lemma to get
157 = 38 x 4 + 5
We consider the new divisor 38 and the new remainder 5,and apply the division lemma to get
38 = 5 x 7 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 823 and 8073 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(38,5) = HCF(157,38) = HCF(666,157) = HCF(823,666) = HCF(8073,823) .
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Frequently Asked Questions on HCF of 823, 8073 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, 8073?
Answer: HCF of 823, 8073 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 823, 8073 using Euclid's Algorithm?
Answer: For arbitrary numbers 823, 8073 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.