Highest Common Factor of 405, 594, 18 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, 594, 18 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 405, 594, 18 is 9 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, 594, 18 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, 594, 18 is 9.
HCF(405, 594, 18) = 9
HCF of 405, 594, 18 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, 594, 18 is 9.
Highest Common Factor of 405,594,18 is 9
Step 1: Since 594 > 405, we apply the division lemma to 594 and 405, to get
594 = 405 x 1 + 189
Step 2: Since the reminder 405 ≠ 0, we apply division lemma to 189 and 405, to get
405 = 189 x 2 + 27
Step 3: We consider the new divisor 189 and the new remainder 27, and apply the division lemma to get
189 = 27 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 405 and 594 is 27
Notice that 27 = HCF(189,27) = HCF(405,189) = HCF(594,405) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 27 > 18, we apply the division lemma to 27 and 18, to get
27 = 18 x 1 + 9
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 9 and 18, to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 27 and 18 is 9
Notice that 9 = HCF(18,9) = HCF(27,18) .
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Frequently Asked Questions on HCF of 405, 594, 18 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, 594, 18?
Answer: HCF of 405, 594, 18 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 405, 594, 18 using Euclid's Algorithm?
Answer: For arbitrary numbers 405, 594, 18 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
