Highest Common Factor of 356, 582, 988 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 356, 582, 988 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 356, 582, 988 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 356, 582, 988 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 356, 582, 988 is 2.
HCF(356, 582, 988) = 2
HCF of 356, 582, 988 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 356, 582, 988 is 2.
Highest Common Factor of 356,582,988 is 2
Step 1: Since 582 > 356, we apply the division lemma to 582 and 356, to get
582 = 356 x 1 + 226
Step 2: Since the reminder 356 ≠ 0, we apply division lemma to 226 and 356, to get
356 = 226 x 1 + 130
Step 3: We consider the new divisor 226 and the new remainder 130, and apply the division lemma to get
226 = 130 x 1 + 96
We consider the new divisor 130 and the new remainder 96,and apply the division lemma to get
130 = 96 x 1 + 34
We consider the new divisor 96 and the new remainder 34,and apply the division lemma to get
96 = 34 x 2 + 28
We consider the new divisor 34 and the new remainder 28,and apply the division lemma to get
34 = 28 x 1 + 6
We consider the new divisor 28 and the new remainder 6,and apply the division lemma to get
28 = 6 x 4 + 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 356 and 582 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(28,6) = HCF(34,28) = HCF(96,34) = HCF(130,96) = HCF(226,130) = HCF(356,226) = HCF(582,356) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 988 > 2, we apply the division lemma to 988 and 2, to get
988 = 2 x 494 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 988 is 2
Notice that 2 = HCF(988,2) .
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Frequently Asked Questions on HCF of 356, 582, 988 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 356, 582, 988?
Answer: HCF of 356, 582, 988 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 356, 582, 988 using Euclid's Algorithm?
Answer: For arbitrary numbers 356, 582, 988 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.