Highest Common Factor of 188, 321, 381 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 188, 321, 381 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 188, 321, 381 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 188, 321, 381 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 188, 321, 381 is 1.
HCF(188, 321, 381) = 1
HCF of 188, 321, 381 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 188, 321, 381 is 1.
Highest Common Factor of 188,321,381 is 1
Step 1: Since 321 > 188, we apply the division lemma to 321 and 188, to get
321 = 188 x 1 + 133
Step 2: Since the reminder 188 ≠ 0, we apply division lemma to 133 and 188, to get
188 = 133 x 1 + 55
Step 3: We consider the new divisor 133 and the new remainder 55, and apply the division lemma to get
133 = 55 x 2 + 23
We consider the new divisor 55 and the new remainder 23,and apply the division lemma to get
55 = 23 x 2 + 9
We consider the new divisor 23 and the new remainder 9,and apply the division lemma to get
23 = 9 x 2 + 5
We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get
9 = 5 x 1 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 188 and 321 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(23,9) = HCF(55,23) = HCF(133,55) = HCF(188,133) = HCF(321,188) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 381 > 1, we apply the division lemma to 381 and 1, to get
381 = 1 x 381 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 381 is 1
Notice that 1 = HCF(381,1) .
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Frequently Asked Questions on HCF of 188, 321, 381 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 188, 321, 381?
Answer: HCF of 188, 321, 381 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 188, 321, 381 using Euclid's Algorithm?
Answer: For arbitrary numbers 188, 321, 381 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.