Highest Common Factor of 957, 396, 417 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 957, 396, 417 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 957, 396, 417 is 3 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 957, 396, 417 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 957, 396, 417 is 3.
HCF(957, 396, 417) = 3
HCF of 957, 396, 417 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 957, 396, 417 is 3.
Highest Common Factor of 957,396,417 is 3
Step 1: Since 957 > 396, we apply the division lemma to 957 and 396, to get
957 = 396 x 2 + 165
Step 2: Since the reminder 396 ≠ 0, we apply division lemma to 165 and 396, to get
396 = 165 x 2 + 66
Step 3: We consider the new divisor 165 and the new remainder 66, and apply the division lemma to get
165 = 66 x 2 + 33
We consider the new divisor 66 and the new remainder 33, and apply the division lemma to get
66 = 33 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 33, the HCF of 957 and 396 is 33
Notice that 33 = HCF(66,33) = HCF(165,66) = HCF(396,165) = HCF(957,396) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 417 > 33, we apply the division lemma to 417 and 33, to get
417 = 33 x 12 + 21
Step 2: Since the reminder 33 ≠ 0, we apply division lemma to 21 and 33, to get
33 = 21 x 1 + 12
Step 3: We consider the new divisor 21 and the new remainder 12, and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 33 and 417 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(33,21) = HCF(417,33) .
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Frequently Asked Questions on HCF of 957, 396, 417 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 957, 396, 417?
Answer: HCF of 957, 396, 417 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 957, 396, 417 using Euclid's Algorithm?
Answer: For arbitrary numbers 957, 396, 417 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.