Highest Common Factor of 213, 603, 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 213, 603, 381 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 213, 603, 381 is 3 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 213, 603, 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 213, 603, 381 is 3.
HCF(213, 603, 381) = 3
HCF of 213, 603, 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 213, 603, 381 is 3.
Highest Common Factor of 213,603,381 is 3
Step 1: Since 603 > 213, we apply the division lemma to 603 and 213, to get
603 = 213 x 2 + 177
Step 2: Since the reminder 213 ≠ 0, we apply division lemma to 177 and 213, to get
213 = 177 x 1 + 36
Step 3: We consider the new divisor 177 and the new remainder 36, and apply the division lemma to get
177 = 36 x 4 + 33
We consider the new divisor 36 and the new remainder 33,and apply the division lemma to get
36 = 33 x 1 + 3
We consider the new divisor 33 and the new remainder 3,and apply the division lemma to get
33 = 3 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 213 and 603 is 3
Notice that 3 = HCF(33,3) = HCF(36,33) = HCF(177,36) = HCF(213,177) = HCF(603,213) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 381 > 3, we apply the division lemma to 381 and 3, to get
381 = 3 x 127 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 381 is 3
Notice that 3 = HCF(381,3) .
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Frequently Asked Questions on HCF of 213, 603, 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 213, 603, 381?
Answer: HCF of 213, 603, 381 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 213, 603, 381 using Euclid's Algorithm?
Answer: For arbitrary numbers 213, 603, 381 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.