Highest Common Factor of 664, 747, 462 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 664, 747, 462 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 664, 747, 462 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 664, 747, 462 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 664, 747, 462 is 1.
HCF(664, 747, 462) = 1
HCF of 664, 747, 462 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 664, 747, 462 is 1.
Highest Common Factor of 664,747,462 is 1
Step 1: Since 747 > 664, we apply the division lemma to 747 and 664, to get
747 = 664 x 1 + 83
Step 2: Since the reminder 664 ≠ 0, we apply division lemma to 83 and 664, to get
664 = 83 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 83, the HCF of 664 and 747 is 83
Notice that 83 = HCF(664,83) = HCF(747,664) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 462 > 83, we apply the division lemma to 462 and 83, to get
462 = 83 x 5 + 47
Step 2: Since the reminder 83 ≠ 0, we apply division lemma to 47 and 83, to get
83 = 47 x 1 + 36
Step 3: We consider the new divisor 47 and the new remainder 36, and apply the division lemma to get
47 = 36 x 1 + 11
We consider the new divisor 36 and the new remainder 11,and apply the division lemma to get
36 = 11 x 3 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 83 and 462 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(36,11) = HCF(47,36) = HCF(83,47) = HCF(462,83) .
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Frequently Asked Questions on HCF of 664, 747, 462 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 664, 747, 462?
Answer: HCF of 664, 747, 462 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 664, 747, 462 using Euclid's Algorithm?
Answer: For arbitrary numbers 664, 747, 462 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.