Highest Common Factor of 729, 771, 109 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, 771, 109 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 729, 771, 109 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, 771, 109 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, 771, 109 is 1.
HCF(729, 771, 109) = 1
HCF of 729, 771, 109 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, 771, 109 is 1.
Highest Common Factor of 729,771,109 is 1
Step 1: Since 771 > 729, we apply the division lemma to 771 and 729, to get
771 = 729 x 1 + 42
Step 2: Since the reminder 729 ≠ 0, we apply division lemma to 42 and 729, to get
729 = 42 x 17 + 15
Step 3: We consider the new divisor 42 and the new remainder 15, and apply the division lemma to get
42 = 15 x 2 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 729 and 771 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(42,15) = HCF(729,42) = HCF(771,729) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 109 > 3, we apply the division lemma to 109 and 3, to get
109 = 3 x 36 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 109 is 1
Notice that 1 = HCF(3,1) = HCF(109,3) .
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, 771, 109 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, 771, 109?
Answer: HCF of 729, 771, 109 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 729, 771, 109 using Euclid's Algorithm?
Answer: For arbitrary numbers 729, 771, 109 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.