Highest Common Factor of 171, 111 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 171, 111 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 171, 111 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 171, 111 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 171, 111 is 3.
HCF(171, 111) = 3
HCF of 171, 111 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 171, 111 is 3.
Highest Common Factor of 171,111 is 3
Step 1: Since 171 > 111, we apply the division lemma to 171 and 111, to get
171 = 111 x 1 + 60
Step 2: Since the reminder 111 ≠ 0, we apply division lemma to 60 and 111, to get
111 = 60 x 1 + 51
Step 3: We consider the new divisor 60 and the new remainder 51, and apply the division lemma to get
60 = 51 x 1 + 9
We consider the new divisor 51 and the new remainder 9,and apply the division lemma to get
51 = 9 x 5 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 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 171 and 111 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(51,9) = HCF(60,51) = HCF(111,60) = HCF(171,111) .
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Frequently Asked Questions on HCF of 171, 111 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 171, 111?
Answer: HCF of 171, 111 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 171, 111 using Euclid's Algorithm?
Answer: For arbitrary numbers 171, 111 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.