Highest Common Factor of 729, 77070 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, 77070 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 729, 77070 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, 77070 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, 77070 is 3.
HCF(729, 77070) = 3
HCF of 729, 77070 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, 77070 is 3.
Highest Common Factor of 729,77070 is 3
Step 1: Since 77070 > 729, we apply the division lemma to 77070 and 729, to get
77070 = 729 x 105 + 525
Step 2: Since the reminder 729 ≠ 0, we apply division lemma to 525 and 729, to get
729 = 525 x 1 + 204
Step 3: We consider the new divisor 525 and the new remainder 204, and apply the division lemma to get
525 = 204 x 2 + 117
We consider the new divisor 204 and the new remainder 117,and apply the division lemma to get
204 = 117 x 1 + 87
We consider the new divisor 117 and the new remainder 87,and apply the division lemma to get
117 = 87 x 1 + 30
We consider the new divisor 87 and the new remainder 30,and apply the division lemma to get
87 = 30 x 2 + 27
We consider the new divisor 30 and the new remainder 27,and apply the division lemma to get
30 = 27 x 1 + 3
We consider the new divisor 27 and the new remainder 3,and apply the division lemma to get
27 = 3 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 729 and 77070 is 3
Notice that 3 = HCF(27,3) = HCF(30,27) = HCF(87,30) = HCF(117,87) = HCF(204,117) = HCF(525,204) = HCF(729,525) = HCF(77070,729) .
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Frequently Asked Questions on HCF of 729, 77070 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, 77070?
Answer: HCF of 729, 77070 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 729, 77070 using Euclid's Algorithm?
Answer: For arbitrary numbers 729, 77070 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.