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, 843, 612 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 729, 843, 612 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, 843, 612 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, 843, 612 is 3.
HCF(729, 843, 612) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 729, 843, 612 is 3.
Step 1: Since 843 > 729, we apply the division lemma to 843 and 729, to get
843 = 729 x 1 + 114
Step 2: Since the reminder 729 ≠ 0, we apply division lemma to 114 and 729, to get
729 = 114 x 6 + 45
Step 3: We consider the new divisor 114 and the new remainder 45, and apply the division lemma to get
114 = 45 x 2 + 24
We consider the new divisor 45 and the new remainder 24,and apply the division lemma to get
45 = 24 x 1 + 21
We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get
24 = 21 x 1 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 729 and 843 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(45,24) = HCF(114,45) = HCF(729,114) = HCF(843,729) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 612 > 3, we apply the division lemma to 612 and 3, to get
612 = 3 x 204 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 612 is 3
Notice that 3 = HCF(612,3) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 843, 612?
Answer: HCF of 729, 843, 612 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 729, 843, 612 using Euclid's Algorithm?
Answer: For arbitrary numbers 729, 843, 612 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.