Highest Common Factor of 366, 69405 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 366, 69405 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 366, 69405 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 366, 69405 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 366, 69405 is 3.
HCF(366, 69405) = 3
HCF of 366, 69405 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 366, 69405 is 3.
Highest Common Factor of 366,69405 is 3
Step 1: Since 69405 > 366, we apply the division lemma to 69405 and 366, to get
69405 = 366 x 189 + 231
Step 2: Since the reminder 366 ≠ 0, we apply division lemma to 231 and 366, to get
366 = 231 x 1 + 135
Step 3: We consider the new divisor 231 and the new remainder 135, and apply the division lemma to get
231 = 135 x 1 + 96
We consider the new divisor 135 and the new remainder 96,and apply the division lemma to get
135 = 96 x 1 + 39
We consider the new divisor 96 and the new remainder 39,and apply the division lemma to get
96 = 39 x 2 + 18
We consider the new divisor 39 and the new remainder 18,and apply the division lemma to get
39 = 18 x 2 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 366 and 69405 is 3
Notice that 3 = HCF(18,3) = HCF(39,18) = HCF(96,39) = HCF(135,96) = HCF(231,135) = HCF(366,231) = HCF(69405,366) .
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Frequently Asked Questions on HCF of 366, 69405 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 366, 69405?
Answer: HCF of 366, 69405 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 366, 69405 using Euclid's Algorithm?
Answer: For arbitrary numbers 366, 69405 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.