Highest Common Factor of 729, 797, 162 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, 797, 162 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 729, 797, 162 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, 797, 162 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, 797, 162 is 1.
HCF(729, 797, 162) = 1
HCF of 729, 797, 162 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, 797, 162 is 1.
Highest Common Factor of 729,797,162 is 1
Step 1: Since 797 > 729, we apply the division lemma to 797 and 729, to get
797 = 729 x 1 + 68
Step 2: Since the reminder 729 ≠ 0, we apply division lemma to 68 and 729, to get
729 = 68 x 10 + 49
Step 3: We consider the new divisor 68 and the new remainder 49, and apply the division lemma to get
68 = 49 x 1 + 19
We consider the new divisor 49 and the new remainder 19,and apply the division lemma to get
49 = 19 x 2 + 11
We consider the new divisor 19 and the new remainder 11,and apply the division lemma to get
19 = 11 x 1 + 8
We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get
11 = 8 x 1 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
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 729 and 797 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(19,11) = HCF(49,19) = HCF(68,49) = HCF(729,68) = HCF(797,729) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 162 > 1, we apply the division lemma to 162 and 1, to get
162 = 1 x 162 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 162 is 1
Notice that 1 = HCF(162,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 729, 797, 162 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, 797, 162?
Answer: HCF of 729, 797, 162 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 729, 797, 162 using Euclid's Algorithm?
Answer: For arbitrary numbers 729, 797, 162 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.