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 3609, 5812, 73641 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3609, 5812, 73641 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 3609, 5812, 73641 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 3609, 5812, 73641 is 1.
HCF(3609, 5812, 73641) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3609, 5812, 73641 is 1.
Step 1: Since 5812 > 3609, we apply the division lemma to 5812 and 3609, to get
5812 = 3609 x 1 + 2203
Step 2: Since the reminder 3609 ≠ 0, we apply division lemma to 2203 and 3609, to get
3609 = 2203 x 1 + 1406
Step 3: We consider the new divisor 2203 and the new remainder 1406, and apply the division lemma to get
2203 = 1406 x 1 + 797
We consider the new divisor 1406 and the new remainder 797,and apply the division lemma to get
1406 = 797 x 1 + 609
We consider the new divisor 797 and the new remainder 609,and apply the division lemma to get
797 = 609 x 1 + 188
We consider the new divisor 609 and the new remainder 188,and apply the division lemma to get
609 = 188 x 3 + 45
We consider the new divisor 188 and the new remainder 45,and apply the division lemma to get
188 = 45 x 4 + 8
We consider the new divisor 45 and the new remainder 8,and apply the division lemma to get
45 = 8 x 5 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 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 3609 and 5812 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(45,8) = HCF(188,45) = HCF(609,188) = HCF(797,609) = HCF(1406,797) = HCF(2203,1406) = HCF(3609,2203) = HCF(5812,3609) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 73641 > 1, we apply the division lemma to 73641 and 1, to get
73641 = 1 x 73641 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 73641 is 1
Notice that 1 = HCF(73641,1) .
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 3609, 5812, 73641?
Answer: HCF of 3609, 5812, 73641 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3609, 5812, 73641 using Euclid's Algorithm?
Answer: For arbitrary numbers 3609, 5812, 73641 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.