Highest Common Factor of 162, 592, 408, 81 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 162, 592, 408, 81 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 162, 592, 408, 81 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 162, 592, 408, 81 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 162, 592, 408, 81 is 1.
HCF(162, 592, 408, 81) = 1
HCF of 162, 592, 408, 81 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 162, 592, 408, 81 is 1.
Highest Common Factor of 162,592,408,81 is 1
Step 1: Since 592 > 162, we apply the division lemma to 592 and 162, to get
592 = 162 x 3 + 106
Step 2: Since the reminder 162 ≠ 0, we apply division lemma to 106 and 162, to get
162 = 106 x 1 + 56
Step 3: We consider the new divisor 106 and the new remainder 56, and apply the division lemma to get
106 = 56 x 1 + 50
We consider the new divisor 56 and the new remainder 50,and apply the division lemma to get
56 = 50 x 1 + 6
We consider the new divisor 50 and the new remainder 6,and apply the division lemma to get
50 = 6 x 8 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 162 and 592 is 2
Notice that 2 = HCF(6,2) = HCF(50,6) = HCF(56,50) = HCF(106,56) = HCF(162,106) = HCF(592,162) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 408 > 2, we apply the division lemma to 408 and 2, to get
408 = 2 x 204 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 408 is 2
Notice that 2 = HCF(408,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 81 > 2, we apply the division lemma to 81 and 2, to get
81 = 2 x 40 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 81 is 1
Notice that 1 = HCF(2,1) = HCF(81,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 162, 592, 408, 81 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 162, 592, 408, 81?
Answer: HCF of 162, 592, 408, 81 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 162, 592, 408, 81 using Euclid's Algorithm?
Answer: For arbitrary numbers 162, 592, 408, 81 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.