Highest Common Factor of 397, 1026 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 397, 1026 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 397, 1026 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 397, 1026 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 397, 1026 is 1.
HCF(397, 1026) = 1
HCF of 397, 1026 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 397, 1026 is 1.
Highest Common Factor of 397,1026 is 1
Step 1: Since 1026 > 397, we apply the division lemma to 1026 and 397, to get
1026 = 397 x 2 + 232
Step 2: Since the reminder 397 ≠ 0, we apply division lemma to 232 and 397, to get
397 = 232 x 1 + 165
Step 3: We consider the new divisor 232 and the new remainder 165, and apply the division lemma to get
232 = 165 x 1 + 67
We consider the new divisor 165 and the new remainder 67,and apply the division lemma to get
165 = 67 x 2 + 31
We consider the new divisor 67 and the new remainder 31,and apply the division lemma to get
67 = 31 x 2 + 5
We consider the new divisor 31 and the new remainder 5,and apply the division lemma to get
31 = 5 x 6 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 397 and 1026 is 1
Notice that 1 = HCF(5,1) = HCF(31,5) = HCF(67,31) = HCF(165,67) = HCF(232,165) = HCF(397,232) = HCF(1026,397) .
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Frequently Asked Questions on HCF of 397, 1026 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 397, 1026?
Answer: HCF of 397, 1026 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 397, 1026 using Euclid's Algorithm?
Answer: For arbitrary numbers 397, 1026 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.