Highest Common Factor of 238, 614 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, 614 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 238, 614 is 2 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, 614 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, 614 is 2.
HCF(238, 614) = 2
HCF of 238, 614 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, 614 is 2.
Highest Common Factor of 238,614 is 2
Step 1: Since 614 > 238, we apply the division lemma to 614 and 238, to get
614 = 238 x 2 + 138
Step 2: Since the reminder 238 ≠ 0, we apply division lemma to 138 and 238, to get
238 = 138 x 1 + 100
Step 3: We consider the new divisor 138 and the new remainder 100, and apply the division lemma to get
138 = 100 x 1 + 38
We consider the new divisor 100 and the new remainder 38,and apply the division lemma to get
100 = 38 x 2 + 24
We consider the new divisor 38 and the new remainder 24,and apply the division lemma to get
38 = 24 x 1 + 14
We consider the new divisor 24 and the new remainder 14,and apply the division lemma to get
24 = 14 x 1 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 238 and 614 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(24,14) = HCF(38,24) = HCF(100,38) = HCF(138,100) = HCF(238,138) = HCF(614,238) .
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Frequently Asked Questions on HCF of 238, 614 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, 614?
Answer: HCF of 238, 614 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 238, 614 using Euclid's Algorithm?
Answer: For arbitrary numbers 238, 614 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.