Highest Common Factor of 459, 693, 321 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, 693, 321 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 459, 693, 321 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, 693, 321 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, 693, 321 is 3.
HCF(459, 693, 321) = 3
HCF of 459, 693, 321 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, 693, 321 is 3.
Highest Common Factor of 459,693,321 is 3
Step 1: Since 693 > 459, we apply the division lemma to 693 and 459, to get
693 = 459 x 1 + 234
Step 2: Since the reminder 459 ≠ 0, we apply division lemma to 234 and 459, to get
459 = 234 x 1 + 225
Step 3: We consider the new divisor 234 and the new remainder 225, and apply the division lemma to get
234 = 225 x 1 + 9
We consider the new divisor 225 and the new remainder 9, and apply the division lemma to get
225 = 9 x 25 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 459 and 693 is 9
Notice that 9 = HCF(225,9) = HCF(234,225) = HCF(459,234) = HCF(693,459) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 321 > 9, we apply the division lemma to 321 and 9, to get
321 = 9 x 35 + 6
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 6 and 9, to get
9 = 6 x 1 + 3
Step 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 9 and 321 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(321,9) .
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Frequently Asked Questions on HCF of 459, 693, 321 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, 693, 321?
Answer: HCF of 459, 693, 321 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 459, 693, 321 using Euclid's Algorithm?
Answer: For arbitrary numbers 459, 693, 321 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.