Highest Common Factor of 462, 723, 667 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 462, 723, 667 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 462, 723, 667 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 462, 723, 667 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 462, 723, 667 is 1.
HCF(462, 723, 667) = 1
HCF of 462, 723, 667 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 462, 723, 667 is 1.
Highest Common Factor of 462,723,667 is 1
Step 1: Since 723 > 462, we apply the division lemma to 723 and 462, to get
723 = 462 x 1 + 261
Step 2: Since the reminder 462 ≠ 0, we apply division lemma to 261 and 462, to get
462 = 261 x 1 + 201
Step 3: We consider the new divisor 261 and the new remainder 201, and apply the division lemma to get
261 = 201 x 1 + 60
We consider the new divisor 201 and the new remainder 60,and apply the division lemma to get
201 = 60 x 3 + 21
We consider the new divisor 60 and the new remainder 21,and apply the division lemma to get
60 = 21 x 2 + 18
We consider the new divisor 21 and the new remainder 18,and apply the division lemma to get
21 = 18 x 1 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 462 and 723 is 3
Notice that 3 = HCF(18,3) = HCF(21,18) = HCF(60,21) = HCF(201,60) = HCF(261,201) = HCF(462,261) = HCF(723,462) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 667 > 3, we apply the division lemma to 667 and 3, to get
667 = 3 x 222 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 667 is 1
Notice that 1 = HCF(3,1) = HCF(667,3) .
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Frequently Asked Questions on HCF of 462, 723, 667 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 462, 723, 667?
Answer: HCF of 462, 723, 667 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 462, 723, 667 using Euclid's Algorithm?
Answer: For arbitrary numbers 462, 723, 667 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.