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, 5962, 4621 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 729, 5962, 4621 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, 5962, 4621 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, 5962, 4621 is 1.
HCF(729, 5962, 4621) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 729, 5962, 4621 is 1.
Step 1: Since 5962 > 729, we apply the division lemma to 5962 and 729, to get
5962 = 729 x 8 + 130
Step 2: Since the reminder 729 ≠ 0, we apply division lemma to 130 and 729, to get
729 = 130 x 5 + 79
Step 3: We consider the new divisor 130 and the new remainder 79, and apply the division lemma to get
130 = 79 x 1 + 51
We consider the new divisor 79 and the new remainder 51,and apply the division lemma to get
79 = 51 x 1 + 28
We consider the new divisor 51 and the new remainder 28,and apply the division lemma to get
51 = 28 x 1 + 23
We consider the new divisor 28 and the new remainder 23,and apply the division lemma to get
28 = 23 x 1 + 5
We consider the new divisor 23 and the new remainder 5,and apply the division lemma to get
23 = 5 x 4 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 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 5962 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(23,5) = HCF(28,23) = HCF(51,28) = HCF(79,51) = HCF(130,79) = HCF(729,130) = HCF(5962,729) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 4621 > 1, we apply the division lemma to 4621 and 1, to get
4621 = 1 x 4621 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 4621 is 1
Notice that 1 = HCF(4621,1) .
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, 5962, 4621?
Answer: HCF of 729, 5962, 4621 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 729, 5962, 4621 using Euclid's Algorithm?
Answer: For arbitrary numbers 729, 5962, 4621 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.