Highest Common Factor of 371, 2093, 1936 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 371, 2093, 1936 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 371, 2093, 1936 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 371, 2093, 1936 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 371, 2093, 1936 is 1.
HCF(371, 2093, 1936) = 1
HCF of 371, 2093, 1936 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 371, 2093, 1936 is 1.
Highest Common Factor of 371,2093,1936 is 1
Step 1: Since 2093 > 371, we apply the division lemma to 2093 and 371, to get
2093 = 371 x 5 + 238
Step 2: Since the reminder 371 ≠ 0, we apply division lemma to 238 and 371, to get
371 = 238 x 1 + 133
Step 3: We consider the new divisor 238 and the new remainder 133, and apply the division lemma to get
238 = 133 x 1 + 105
We consider the new divisor 133 and the new remainder 105,and apply the division lemma to get
133 = 105 x 1 + 28
We consider the new divisor 105 and the new remainder 28,and apply the division lemma to get
105 = 28 x 3 + 21
We consider the new divisor 28 and the new remainder 21,and apply the division lemma to get
28 = 21 x 1 + 7
We consider the new divisor 21 and the new remainder 7,and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 371 and 2093 is 7
Notice that 7 = HCF(21,7) = HCF(28,21) = HCF(105,28) = HCF(133,105) = HCF(238,133) = HCF(371,238) = HCF(2093,371) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1936 > 7, we apply the division lemma to 1936 and 7, to get
1936 = 7 x 276 + 4
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 4 and 7, to get
7 = 4 x 1 + 3
Step 3: We consider the new divisor 4 and the new remainder 3, and apply the division lemma to get
4 = 3 x 1 + 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 7 and 1936 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(1936,7) .
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Frequently Asked Questions on HCF of 371, 2093, 1936 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 371, 2093, 1936?
Answer: HCF of 371, 2093, 1936 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 371, 2093, 1936 using Euclid's Algorithm?
Answer: For arbitrary numbers 371, 2093, 1936 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.