Highest Common Factor of 996, 729, 32 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 996, 729, 32 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 996, 729, 32 is 1 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 996, 729, 32 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 996, 729, 32 is 1.
HCF(996, 729, 32) = 1
HCF of 996, 729, 32 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 996, 729, 32 is 1.
Highest Common Factor of 996,729,32 is 1
Step 1: Since 996 > 729, we apply the division lemma to 996 and 729, to get
996 = 729 x 1 + 267
Step 2: Since the reminder 729 ≠ 0, we apply division lemma to 267 and 729, to get
729 = 267 x 2 + 195
Step 3: We consider the new divisor 267 and the new remainder 195, and apply the division lemma to get
267 = 195 x 1 + 72
We consider the new divisor 195 and the new remainder 72,and apply the division lemma to get
195 = 72 x 2 + 51
We consider the new divisor 72 and the new remainder 51,and apply the division lemma to get
72 = 51 x 1 + 21
We consider the new divisor 51 and the new remainder 21,and apply the division lemma to get
51 = 21 x 2 + 9
We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get
21 = 9 x 2 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 996 and 729 is 3
Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(51,21) = HCF(72,51) = HCF(195,72) = HCF(267,195) = HCF(729,267) = HCF(996,729) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 32 > 3, we apply the division lemma to 32 and 3, to get
32 = 3 x 10 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 32 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(32,3) .
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Frequently Asked Questions on HCF of 996, 729, 32 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 996, 729, 32?
Answer: HCF of 996, 729, 32 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 996, 729, 32 using Euclid's Algorithm?
Answer: For arbitrary numbers 996, 729, 32 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.