Highest Common Factor of 729, 921 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, 921 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 729, 921 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, 921 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, 921 is 3.
HCF(729, 921) = 3
HCF of 729, 921 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, 921 is 3.
Highest Common Factor of 729,921 is 3
Step 1: Since 921 > 729, we apply the division lemma to 921 and 729, to get
921 = 729 x 1 + 192
Step 2: Since the reminder 729 ≠ 0, we apply division lemma to 192 and 729, to get
729 = 192 x 3 + 153
Step 3: We consider the new divisor 192 and the new remainder 153, and apply the division lemma to get
192 = 153 x 1 + 39
We consider the new divisor 153 and the new remainder 39,and apply the division lemma to get
153 = 39 x 3 + 36
We consider the new divisor 39 and the new remainder 36,and apply the division lemma to get
39 = 36 x 1 + 3
We consider the new divisor 36 and the new remainder 3,and apply the division lemma to get
36 = 3 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 729 and 921 is 3
Notice that 3 = HCF(36,3) = HCF(39,36) = HCF(153,39) = HCF(192,153) = HCF(729,192) = HCF(921,729) .
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Frequently Asked Questions on HCF of 729, 921 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, 921?
Answer: HCF of 729, 921 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 729, 921 using Euclid's Algorithm?
Answer: For arbitrary numbers 729, 921 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.