Highest Common Factor of 459, 582, 162 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 459, 582, 162 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 459, 582, 162 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 459, 582, 162 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 459, 582, 162 is 3.
HCF(459, 582, 162) = 3
HCF of 459, 582, 162 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 459, 582, 162 is 3.
Highest Common Factor of 459,582,162 is 3
Step 1: Since 582 > 459, we apply the division lemma to 582 and 459, to get
582 = 459 x 1 + 123
Step 2: Since the reminder 459 ≠ 0, we apply division lemma to 123 and 459, to get
459 = 123 x 3 + 90
Step 3: We consider the new divisor 123 and the new remainder 90, and apply the division lemma to get
123 = 90 x 1 + 33
We consider the new divisor 90 and the new remainder 33,and apply the division lemma to get
90 = 33 x 2 + 24
We consider the new divisor 33 and the new remainder 24,and apply the division lemma to get
33 = 24 x 1 + 9
We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get
24 = 9 x 2 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 459 and 582 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(33,24) = HCF(90,33) = HCF(123,90) = HCF(459,123) = HCF(582,459) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 162 > 3, we apply the division lemma to 162 and 3, to get
162 = 3 x 54 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 162 is 3
Notice that 3 = HCF(162,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 459, 582, 162 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 459, 582, 162?
Answer: HCF of 459, 582, 162 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 459, 582, 162 using Euclid's Algorithm?
Answer: For arbitrary numbers 459, 582, 162 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.