Highest Common Factor of 405, 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 405, 111 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 405, 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 405, 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 405, 111 is 3.
HCF(405, 111) = 3
HCF of 405, 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 405, 111 is 3.
Highest Common Factor of 405,111 is 3
Step 1: Since 405 > 111, we apply the division lemma to 405 and 111, to get
405 = 111 x 3 + 72
Step 2: Since the reminder 111 ≠ 0, we apply division lemma to 72 and 111, to get
111 = 72 x 1 + 39
Step 3: We consider the new divisor 72 and the new remainder 39, and apply the division lemma to get
72 = 39 x 1 + 33
We consider the new divisor 39 and the new remainder 33,and apply the division lemma to get
39 = 33 x 1 + 6
We consider the new divisor 33 and the new remainder 6,and apply the division lemma to get
33 = 6 x 5 + 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 405 and 111 is 3
Notice that 3 = HCF(6,3) = HCF(33,6) = HCF(39,33) = HCF(72,39) = HCF(111,72) = HCF(405,111) .
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Frequently Asked Questions on HCF of 405, 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 405, 111?
Answer: HCF of 405, 111 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 405, 111 using Euclid's Algorithm?
Answer: For arbitrary numbers 405, 111 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.