Highest Common Factor of 824, 997 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 824, 997 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 824, 997 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 824, 997 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 824, 997 is 1.
HCF(824, 997) = 1
HCF of 824, 997 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 824, 997 is 1.
Highest Common Factor of 824,997 is 1
Step 1: Since 997 > 824, we apply the division lemma to 997 and 824, to get
997 = 824 x 1 + 173
Step 2: Since the reminder 824 ≠ 0, we apply division lemma to 173 and 824, to get
824 = 173 x 4 + 132
Step 3: We consider the new divisor 173 and the new remainder 132, and apply the division lemma to get
173 = 132 x 1 + 41
We consider the new divisor 132 and the new remainder 41,and apply the division lemma to get
132 = 41 x 3 + 9
We consider the new divisor 41 and the new remainder 9,and apply the division lemma to get
41 = 9 x 4 + 5
We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get
9 = 5 x 1 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 824 and 997 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(41,9) = HCF(132,41) = HCF(173,132) = HCF(824,173) = HCF(997,824) .
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Frequently Asked Questions on HCF of 824, 997 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 824, 997?
Answer: HCF of 824, 997 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 824, 997 using Euclid's Algorithm?
Answer: For arbitrary numbers 824, 997 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.