Highest Common Factor of 459, 165, 420 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, 165, 420 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 459, 165, 420 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, 165, 420 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, 165, 420 is 3.
HCF(459, 165, 420) = 3
HCF of 459, 165, 420 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, 165, 420 is 3.
Highest Common Factor of 459,165,420 is 3
Step 1: Since 459 > 165, we apply the division lemma to 459 and 165, to get
459 = 165 x 2 + 129
Step 2: Since the reminder 165 ≠ 0, we apply division lemma to 129 and 165, to get
165 = 129 x 1 + 36
Step 3: We consider the new divisor 129 and the new remainder 36, and apply the division lemma to get
129 = 36 x 3 + 21
We consider the new divisor 36 and the new remainder 21,and apply the division lemma to get
36 = 21 x 1 + 15
We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get
21 = 15 x 1 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 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 165 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(36,21) = HCF(129,36) = HCF(165,129) = HCF(459,165) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 420 > 3, we apply the division lemma to 420 and 3, to get
420 = 3 x 140 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 420 is 3
Notice that 3 = HCF(420,3) .
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Frequently Asked Questions on HCF of 459, 165, 420 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, 165, 420?
Answer: HCF of 459, 165, 420 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 459, 165, 420 using Euclid's Algorithm?
Answer: For arbitrary numbers 459, 165, 420 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.