Highest Common Factor of 403, 912, 817 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, 912, 817 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 403, 912, 817 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, 912, 817 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, 912, 817 is 1.
HCF(403, 912, 817) = 1
HCF of 403, 912, 817 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, 912, 817 is 1.
Highest Common Factor of 403,912,817 is 1
Step 1: Since 912 > 403, we apply the division lemma to 912 and 403, to get
912 = 403 x 2 + 106
Step 2: Since the reminder 403 ≠ 0, we apply division lemma to 106 and 403, to get
403 = 106 x 3 + 85
Step 3: We consider the new divisor 106 and the new remainder 85, and apply the division lemma to get
106 = 85 x 1 + 21
We consider the new divisor 85 and the new remainder 21,and apply the division lemma to get
85 = 21 x 4 + 1
We consider the new divisor 21 and the new remainder 1,and apply the division lemma to get
21 = 1 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 403 and 912 is 1
Notice that 1 = HCF(21,1) = HCF(85,21) = HCF(106,85) = HCF(403,106) = HCF(912,403) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 817 > 1, we apply the division lemma to 817 and 1, to get
817 = 1 x 817 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 817 is 1
Notice that 1 = HCF(817,1) .
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Frequently Asked Questions on HCF of 403, 912, 817 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, 912, 817?
Answer: HCF of 403, 912, 817 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 403, 912, 817 using Euclid's Algorithm?
Answer: For arbitrary numbers 403, 912, 817 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.