Highest Common Factor of 916, 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 916, 582 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 916, 582 is 2 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 916, 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 916, 582 is 2.
HCF(916, 582) = 2
HCF of 916, 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 916, 582 is 2.
Highest Common Factor of 916,582 is 2
Step 1: Since 916 > 582, we apply the division lemma to 916 and 582, to get
916 = 582 x 1 + 334
Step 2: Since the reminder 582 ≠ 0, we apply division lemma to 334 and 582, to get
582 = 334 x 1 + 248
Step 3: We consider the new divisor 334 and the new remainder 248, and apply the division lemma to get
334 = 248 x 1 + 86
We consider the new divisor 248 and the new remainder 86,and apply the division lemma to get
248 = 86 x 2 + 76
We consider the new divisor 86 and the new remainder 76,and apply the division lemma to get
86 = 76 x 1 + 10
We consider the new divisor 76 and the new remainder 10,and apply the division lemma to get
76 = 10 x 7 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 916 and 582 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(76,10) = HCF(86,76) = HCF(248,86) = HCF(334,248) = HCF(582,334) = HCF(916,582) .
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Frequently Asked Questions on HCF of 916, 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 916, 582?
Answer: HCF of 916, 582 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 916, 582 using Euclid's Algorithm?
Answer: For arbitrary numbers 916, 582 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.