Highest Common Factor of 667, 923, 82 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 667, 923, 82 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 667, 923, 82 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 667, 923, 82 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 667, 923, 82 is 1.
HCF(667, 923, 82) = 1
HCF of 667, 923, 82 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 667, 923, 82 is 1.
Highest Common Factor of 667,923,82 is 1
Step 1: Since 923 > 667, we apply the division lemma to 923 and 667, to get
923 = 667 x 1 + 256
Step 2: Since the reminder 667 ≠ 0, we apply division lemma to 256 and 667, to get
667 = 256 x 2 + 155
Step 3: We consider the new divisor 256 and the new remainder 155, and apply the division lemma to get
256 = 155 x 1 + 101
We consider the new divisor 155 and the new remainder 101,and apply the division lemma to get
155 = 101 x 1 + 54
We consider the new divisor 101 and the new remainder 54,and apply the division lemma to get
101 = 54 x 1 + 47
We consider the new divisor 54 and the new remainder 47,and apply the division lemma to get
54 = 47 x 1 + 7
We consider the new divisor 47 and the new remainder 7,and apply the division lemma to get
47 = 7 x 6 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 667 and 923 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(47,7) = HCF(54,47) = HCF(101,54) = HCF(155,101) = HCF(256,155) = HCF(667,256) = HCF(923,667) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 82 > 1, we apply the division lemma to 82 and 1, to get
82 = 1 x 82 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 82 is 1
Notice that 1 = HCF(82,1) .
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Frequently Asked Questions on HCF of 667, 923, 82 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 667, 923, 82?
Answer: HCF of 667, 923, 82 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 667, 923, 82 using Euclid's Algorithm?
Answer: For arbitrary numbers 667, 923, 82 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
