Highest Common Factor of 216, 977, 582 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 216, 977, 582 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 216, 977, 582 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 216, 977, 582 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 216, 977, 582 is 1.
HCF(216, 977, 582) = 1
HCF of 216, 977, 582 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 216, 977, 582 is 1.
Highest Common Factor of 216,977,582 is 1
Step 1: Since 977 > 216, we apply the division lemma to 977 and 216, to get
977 = 216 x 4 + 113
Step 2: Since the reminder 216 ≠ 0, we apply division lemma to 113 and 216, to get
216 = 113 x 1 + 103
Step 3: We consider the new divisor 113 and the new remainder 103, and apply the division lemma to get
113 = 103 x 1 + 10
We consider the new divisor 103 and the new remainder 10,and apply the division lemma to get
103 = 10 x 10 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 216 and 977 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(103,10) = HCF(113,103) = HCF(216,113) = HCF(977,216) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 582 > 1, we apply the division lemma to 582 and 1, to get
582 = 1 x 582 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 582 is 1
Notice that 1 = HCF(582,1) .
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Frequently Asked Questions on HCF of 216, 977, 582 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 216, 977, 582?
Answer: HCF of 216, 977, 582 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 216, 977, 582 using Euclid's Algorithm?
Answer: For arbitrary numbers 216, 977, 582 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.