Highest Common Factor of 582, 991, 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 582, 991, 82 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 582, 991, 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 582, 991, 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 582, 991, 82 is 1.
HCF(582, 991, 82) = 1
HCF of 582, 991, 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 582, 991, 82 is 1.
Highest Common Factor of 582,991,82 is 1
Step 1: Since 991 > 582, we apply the division lemma to 991 and 582, to get
991 = 582 x 1 + 409
Step 2: Since the reminder 582 ≠ 0, we apply division lemma to 409 and 582, to get
582 = 409 x 1 + 173
Step 3: We consider the new divisor 409 and the new remainder 173, and apply the division lemma to get
409 = 173 x 2 + 63
We consider the new divisor 173 and the new remainder 63,and apply the division lemma to get
173 = 63 x 2 + 47
We consider the new divisor 63 and the new remainder 47,and apply the division lemma to get
63 = 47 x 1 + 16
We consider the new divisor 47 and the new remainder 16,and apply the division lemma to get
47 = 16 x 2 + 15
We consider the new divisor 16 and the new remainder 15,and apply the division lemma to get
16 = 15 x 1 + 1
We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 582 and 991 is 1
Notice that 1 = HCF(15,1) = HCF(16,15) = HCF(47,16) = HCF(63,47) = HCF(173,63) = HCF(409,173) = HCF(582,409) = HCF(991,582) .
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 582, 991, 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 582, 991, 82?
Answer: HCF of 582, 991, 82 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 582, 991, 82 using Euclid's Algorithm?
Answer: For arbitrary numbers 582, 991, 82 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.