Highest Common Factor of 729, 864, 645 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, 864, 645 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 729, 864, 645 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, 864, 645 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, 864, 645 is 3.
HCF(729, 864, 645) = 3
HCF of 729, 864, 645 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, 864, 645 is 3.
Highest Common Factor of 729,864,645 is 3
Step 1: Since 864 > 729, we apply the division lemma to 864 and 729, to get
864 = 729 x 1 + 135
Step 2: Since the reminder 729 ≠ 0, we apply division lemma to 135 and 729, to get
729 = 135 x 5 + 54
Step 3: We consider the new divisor 135 and the new remainder 54, and apply the division lemma to get
135 = 54 x 2 + 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 864 is 27
Notice that 27 = HCF(54,27) = HCF(135,54) = HCF(729,135) = HCF(864,729) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 645 > 27, we apply the division lemma to 645 and 27, to get
645 = 27 x 23 + 24
Step 2: Since the reminder 27 ≠ 0, we apply division lemma to 24 and 27, to get
27 = 24 x 1 + 3
Step 3: We consider the new divisor 24 and the new remainder 3, and apply the division lemma to get
24 = 3 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 27 and 645 is 3
Notice that 3 = HCF(24,3) = HCF(27,24) = HCF(645,27) .
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Frequently Asked Questions on HCF of 729, 864, 645 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, 864, 645?
Answer: HCF of 729, 864, 645 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 729, 864, 645 using Euclid's Algorithm?
Answer: For arbitrary numbers 729, 864, 645 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
