Highest Common Factor of 403, 10417 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 403, 10417 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 403, 10417 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 403, 10417 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 403, 10417 is 1.
HCF(403, 10417) = 1
HCF of 403, 10417 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 403, 10417 is 1.
Highest Common Factor of 403,10417 is 1
Step 1: Since 10417 > 403, we apply the division lemma to 10417 and 403, to get
10417 = 403 x 25 + 342
Step 2: Since the reminder 403 ≠ 0, we apply division lemma to 342 and 403, to get
403 = 342 x 1 + 61
Step 3: We consider the new divisor 342 and the new remainder 61, and apply the division lemma to get
342 = 61 x 5 + 37
We consider the new divisor 61 and the new remainder 37,and apply the division lemma to get
61 = 37 x 1 + 24
We consider the new divisor 37 and the new remainder 24,and apply the division lemma to get
37 = 24 x 1 + 13
We consider the new divisor 24 and the new remainder 13,and apply the division lemma to get
24 = 13 x 1 + 11
We consider the new divisor 13 and the new remainder 11,and apply the division lemma to get
13 = 11 x 1 + 2
We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get
11 = 2 x 5 + 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 403 and 10417 is 1
Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(24,13) = HCF(37,24) = HCF(61,37) = HCF(342,61) = HCF(403,342) = HCF(10417,403) .
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Frequently Asked Questions on HCF of 403, 10417 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 403, 10417?
Answer: HCF of 403, 10417 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 403, 10417 using Euclid's Algorithm?
Answer: For arbitrary numbers 403, 10417 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
