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, 1016, 74073 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3609, 1016, 74073 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, 1016, 74073 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, 1016, 74073 is 1.
HCF(3609, 1016, 74073) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3609, 1016, 74073 is 1.
Step 1: Since 3609 > 1016, we apply the division lemma to 3609 and 1016, to get
3609 = 1016 x 3 + 561
Step 2: Since the reminder 1016 ≠ 0, we apply division lemma to 561 and 1016, to get
1016 = 561 x 1 + 455
Step 3: We consider the new divisor 561 and the new remainder 455, and apply the division lemma to get
561 = 455 x 1 + 106
We consider the new divisor 455 and the new remainder 106,and apply the division lemma to get
455 = 106 x 4 + 31
We consider the new divisor 106 and the new remainder 31,and apply the division lemma to get
106 = 31 x 3 + 13
We consider the new divisor 31 and the new remainder 13,and apply the division lemma to get
31 = 13 x 2 + 5
We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get
13 = 5 x 2 + 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 1016 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(31,13) = HCF(106,31) = HCF(455,106) = HCF(561,455) = HCF(1016,561) = HCF(3609,1016) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 74073 > 1, we apply the division lemma to 74073 and 1, to get
74073 = 1 x 74073 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 74073 is 1
Notice that 1 = HCF(74073,1) .
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, 1016, 74073?
Answer: HCF of 3609, 1016, 74073 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3609, 1016, 74073 using Euclid's Algorithm?
Answer: For arbitrary numbers 3609, 1016, 74073 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.