Highest Common Factor of 411, 161, 54 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 411, 161, 54 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 411, 161, 54 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 411, 161, 54 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 411, 161, 54 is 1.
HCF(411, 161, 54) = 1
HCF of 411, 161, 54 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 411, 161, 54 is 1.
Highest Common Factor of 411,161,54 is 1
Step 1: Since 411 > 161, we apply the division lemma to 411 and 161, to get
411 = 161 x 2 + 89
Step 2: Since the reminder 161 ≠ 0, we apply division lemma to 89 and 161, to get
161 = 89 x 1 + 72
Step 3: We consider the new divisor 89 and the new remainder 72, and apply the division lemma to get
89 = 72 x 1 + 17
We consider the new divisor 72 and the new remainder 17,and apply the division lemma to get
72 = 17 x 4 + 4
We consider the new divisor 17 and the new remainder 4,and apply the division lemma to get
17 = 4 x 4 + 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 411 and 161 is 1
Notice that 1 = HCF(4,1) = HCF(17,4) = HCF(72,17) = HCF(89,72) = HCF(161,89) = HCF(411,161) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 54 > 1, we apply the division lemma to 54 and 1, to get
54 = 1 x 54 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 54 is 1
Notice that 1 = HCF(54,1) .
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Frequently Asked Questions on HCF of 411, 161, 54 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 411, 161, 54?
Answer: HCF of 411, 161, 54 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 411, 161, 54 using Euclid's Algorithm?
Answer: For arbitrary numbers 411, 161, 54 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
