Highest Common Factor of 582, 946, 416 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, 946, 416 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 582, 946, 416 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 582, 946, 416 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, 946, 416 is 2.
HCF(582, 946, 416) = 2
HCF of 582, 946, 416 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, 946, 416 is 2.
Highest Common Factor of 582,946,416 is 2
Step 1: Since 946 > 582, we apply the division lemma to 946 and 582, to get
946 = 582 x 1 + 364
Step 2: Since the reminder 582 ≠ 0, we apply division lemma to 364 and 582, to get
582 = 364 x 1 + 218
Step 3: We consider the new divisor 364 and the new remainder 218, and apply the division lemma to get
364 = 218 x 1 + 146
We consider the new divisor 218 and the new remainder 146,and apply the division lemma to get
218 = 146 x 1 + 72
We consider the new divisor 146 and the new remainder 72,and apply the division lemma to get
146 = 72 x 2 + 2
We consider the new divisor 72 and the new remainder 2,and apply the division lemma to get
72 = 2 x 36 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 582 and 946 is 2
Notice that 2 = HCF(72,2) = HCF(146,72) = HCF(218,146) = HCF(364,218) = HCF(582,364) = HCF(946,582) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 416 > 2, we apply the division lemma to 416 and 2, to get
416 = 2 x 208 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 416 is 2
Notice that 2 = HCF(416,2) .
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Frequently Asked Questions on HCF of 582, 946, 416 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, 946, 416?
Answer: HCF of 582, 946, 416 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 582, 946, 416 using Euclid's Algorithm?
Answer: For arbitrary numbers 582, 946, 416 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.