Highest Common Factor of 238, 612, 423 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 238, 612, 423 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 238, 612, 423 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 238, 612, 423 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 238, 612, 423 is 1.
HCF(238, 612, 423) = 1
HCF of 238, 612, 423 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 238, 612, 423 is 1.
Highest Common Factor of 238,612,423 is 1
Step 1: Since 612 > 238, we apply the division lemma to 612 and 238, to get
612 = 238 x 2 + 136
Step 2: Since the reminder 238 ≠ 0, we apply division lemma to 136 and 238, to get
238 = 136 x 1 + 102
Step 3: We consider the new divisor 136 and the new remainder 102, and apply the division lemma to get
136 = 102 x 1 + 34
We consider the new divisor 102 and the new remainder 34, and apply the division lemma to get
102 = 34 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 34, the HCF of 238 and 612 is 34
Notice that 34 = HCF(102,34) = HCF(136,102) = HCF(238,136) = HCF(612,238) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 423 > 34, we apply the division lemma to 423 and 34, to get
423 = 34 x 12 + 15
Step 2: Since the reminder 34 ≠ 0, we apply division lemma to 15 and 34, to get
34 = 15 x 2 + 4
Step 3: We consider the new divisor 15 and the new remainder 4, and apply the division lemma to get
15 = 4 x 3 + 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 34 and 423 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(34,15) = HCF(423,34) .
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Frequently Asked Questions on HCF of 238, 612, 423 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 238, 612, 423?
Answer: HCF of 238, 612, 423 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 238, 612, 423 using Euclid's Algorithm?
Answer: For arbitrary numbers 238, 612, 423 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.