Highest Common Factor of 234, 417 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 234, 417 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 234, 417 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 234, 417 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 234, 417 is 3.
HCF(234, 417) = 3
HCF of 234, 417 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 234, 417 is 3.
Highest Common Factor of 234,417 is 3
Step 1: Since 417 > 234, we apply the division lemma to 417 and 234, to get
417 = 234 x 1 + 183
Step 2: Since the reminder 234 ≠ 0, we apply division lemma to 183 and 234, to get
234 = 183 x 1 + 51
Step 3: We consider the new divisor 183 and the new remainder 51, and apply the division lemma to get
183 = 51 x 3 + 30
We consider the new divisor 51 and the new remainder 30,and apply the division lemma to get
51 = 30 x 1 + 21
We consider the new divisor 30 and the new remainder 21,and apply the division lemma to get
30 = 21 x 1 + 9
We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get
21 = 9 x 2 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 234 and 417 is 3
Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(30,21) = HCF(51,30) = HCF(183,51) = HCF(234,183) = HCF(417,234) .
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Frequently Asked Questions on HCF of 234, 417 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 234, 417?
Answer: HCF of 234, 417 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 234, 417 using Euclid's Algorithm?
Answer: For arbitrary numbers 234, 417 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.