Highest Common Factor of 729, 216, 285 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 729, 216, 285 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 729, 216, 285 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 729, 216, 285 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 729, 216, 285 is 3.
HCF(729, 216, 285) = 3
HCF of 729, 216, 285 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 729, 216, 285 is 3.
Highest Common Factor of 729,216,285 is 3
Step 1: Since 729 > 216, we apply the division lemma to 729 and 216, to get
729 = 216 x 3 + 81
Step 2: Since the reminder 216 ≠ 0, we apply division lemma to 81 and 216, to get
216 = 81 x 2 + 54
Step 3: We consider the new divisor 81 and the new remainder 54, and apply the division lemma to get
81 = 54 x 1 + 27
We consider the new divisor 54 and the new remainder 27, and apply the division lemma to get
54 = 27 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 729 and 216 is 27
Notice that 27 = HCF(54,27) = HCF(81,54) = HCF(216,81) = HCF(729,216) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 285 > 27, we apply the division lemma to 285 and 27, to get
285 = 27 x 10 + 15
Step 2: Since the reminder 27 ≠ 0, we apply division lemma to 15 and 27, to get
27 = 15 x 1 + 12
Step 3: We consider the new divisor 15 and the new remainder 12, and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3, and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 27 and 285 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(27,15) = HCF(285,27) .
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Frequently Asked Questions on HCF of 729, 216, 285 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 729, 216, 285?
Answer: HCF of 729, 216, 285 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 729, 216, 285 using Euclid's Algorithm?
Answer: For arbitrary numbers 729, 216, 285 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.