Highest Common Factor of 729, 9205 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, 9205 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 729, 9205 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 729, 9205 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, 9205 is 1.
HCF(729, 9205) = 1
HCF of 729, 9205 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, 9205 is 1.
Highest Common Factor of 729,9205 is 1
Step 1: Since 9205 > 729, we apply the division lemma to 9205 and 729, to get
9205 = 729 x 12 + 457
Step 2: Since the reminder 729 ≠ 0, we apply division lemma to 457 and 729, to get
729 = 457 x 1 + 272
Step 3: We consider the new divisor 457 and the new remainder 272, and apply the division lemma to get
457 = 272 x 1 + 185
We consider the new divisor 272 and the new remainder 185,and apply the division lemma to get
272 = 185 x 1 + 87
We consider the new divisor 185 and the new remainder 87,and apply the division lemma to get
185 = 87 x 2 + 11
We consider the new divisor 87 and the new remainder 11,and apply the division lemma to get
87 = 11 x 7 + 10
We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get
11 = 10 x 1 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 729 and 9205 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(87,11) = HCF(185,87) = HCF(272,185) = HCF(457,272) = HCF(729,457) = HCF(9205,729) .
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Frequently Asked Questions on HCF of 729, 9205 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, 9205?
Answer: HCF of 729, 9205 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 729, 9205 using Euclid's Algorithm?
Answer: For arbitrary numbers 729, 9205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
