Highest Common Factor of 368, 582, 106, 27 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 368, 582, 106, 27 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 368, 582, 106, 27 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 368, 582, 106, 27 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 368, 582, 106, 27 is 1.
HCF(368, 582, 106, 27) = 1
HCF of 368, 582, 106, 27 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 368, 582, 106, 27 is 1.
Highest Common Factor of 368,582,106,27 is 1
Step 1: Since 582 > 368, we apply the division lemma to 582 and 368, to get
582 = 368 x 1 + 214
Step 2: Since the reminder 368 ≠ 0, we apply division lemma to 214 and 368, to get
368 = 214 x 1 + 154
Step 3: We consider the new divisor 214 and the new remainder 154, and apply the division lemma to get
214 = 154 x 1 + 60
We consider the new divisor 154 and the new remainder 60,and apply the division lemma to get
154 = 60 x 2 + 34
We consider the new divisor 60 and the new remainder 34,and apply the division lemma to get
60 = 34 x 1 + 26
We consider the new divisor 34 and the new remainder 26,and apply the division lemma to get
34 = 26 x 1 + 8
We consider the new divisor 26 and the new remainder 8,and apply the division lemma to get
26 = 8 x 3 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 368 and 582 is 2
Notice that 2 = HCF(8,2) = HCF(26,8) = HCF(34,26) = HCF(60,34) = HCF(154,60) = HCF(214,154) = HCF(368,214) = HCF(582,368) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 106 > 2, we apply the division lemma to 106 and 2, to get
106 = 2 x 53 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 106 is 2
Notice that 2 = HCF(106,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 27 > 2, we apply the division lemma to 27 and 2, to get
27 = 2 x 13 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 27 is 1
Notice that 1 = HCF(2,1) = HCF(27,2) .
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Frequently Asked Questions on HCF of 368, 582, 106, 27 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 368, 582, 106, 27?
Answer: HCF of 368, 582, 106, 27 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 368, 582, 106, 27 using Euclid's Algorithm?
Answer: For arbitrary numbers 368, 582, 106, 27 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.