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 475, 7232, 3093 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 475, 7232, 3093 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 475, 7232, 3093 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 475, 7232, 3093 is 1.
HCF(475, 7232, 3093) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 475, 7232, 3093 is 1.
Step 1: Since 7232 > 475, we apply the division lemma to 7232 and 475, to get
7232 = 475 x 15 + 107
Step 2: Since the reminder 475 ≠ 0, we apply division lemma to 107 and 475, to get
475 = 107 x 4 + 47
Step 3: We consider the new divisor 107 and the new remainder 47, and apply the division lemma to get
107 = 47 x 2 + 13
We consider the new divisor 47 and the new remainder 13,and apply the division lemma to get
47 = 13 x 3 + 8
We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get
13 = 8 x 1 + 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 475 and 7232 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(47,13) = HCF(107,47) = HCF(475,107) = HCF(7232,475) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3093 > 1, we apply the division lemma to 3093 and 1, to get
3093 = 1 x 3093 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 3093 is 1
Notice that 1 = HCF(3093,1) .
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 475, 7232, 3093?
Answer: HCF of 475, 7232, 3093 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 475, 7232, 3093 using Euclid's Algorithm?
Answer: For arbitrary numbers 475, 7232, 3093 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.