Highest Common Factor of 261, 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 261, 417 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 261, 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 261, 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 261, 417 is 3.
HCF(261, 417) = 3
HCF of 261, 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 261, 417 is 3.
Highest Common Factor of 261,417 is 3
Step 1: Since 417 > 261, we apply the division lemma to 417 and 261, to get
417 = 261 x 1 + 156
Step 2: Since the reminder 261 ≠ 0, we apply division lemma to 156 and 261, to get
261 = 156 x 1 + 105
Step 3: We consider the new divisor 156 and the new remainder 105, and apply the division lemma to get
156 = 105 x 1 + 51
We consider the new divisor 105 and the new remainder 51,and apply the division lemma to get
105 = 51 x 2 + 3
We consider the new divisor 51 and the new remainder 3,and apply the division lemma to get
51 = 3 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 261 and 417 is 3
Notice that 3 = HCF(51,3) = HCF(105,51) = HCF(156,105) = HCF(261,156) = HCF(417,261) .
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Frequently Asked Questions on HCF of 261, 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 261, 417?
Answer: HCF of 261, 417 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 261, 417 using Euclid's Algorithm?
Answer: For arbitrary numbers 261, 417 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.