Highest Common Factor of 261, 171, 501 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, 171, 501 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 261, 171, 501 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, 171, 501 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, 171, 501 is 3.
HCF(261, 171, 501) = 3
HCF of 261, 171, 501 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, 171, 501 is 3.
Highest Common Factor of 261,171,501 is 3
Step 1: Since 261 > 171, we apply the division lemma to 261 and 171, to get
261 = 171 x 1 + 90
Step 2: Since the reminder 171 ≠ 0, we apply division lemma to 90 and 171, to get
171 = 90 x 1 + 81
Step 3: We consider the new divisor 90 and the new remainder 81, and apply the division lemma to get
90 = 81 x 1 + 9
We consider the new divisor 81 and the new remainder 9, and apply the division lemma to get
81 = 9 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 261 and 171 is 9
Notice that 9 = HCF(81,9) = HCF(90,81) = HCF(171,90) = HCF(261,171) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 501 > 9, we apply the division lemma to 501 and 9, to get
501 = 9 x 55 + 6
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 6 and 9, to get
9 = 6 x 1 + 3
Step 3: We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9 and 501 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(501,9) .
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Frequently Asked Questions on HCF of 261, 171, 501 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, 171, 501?
Answer: HCF of 261, 171, 501 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 261, 171, 501 using Euclid's Algorithm?
Answer: For arbitrary numbers 261, 171, 501 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.