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 1784, 4438, 20157 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1784, 4438, 20157 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 1784, 4438, 20157 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 1784, 4438, 20157 is 1.
HCF(1784, 4438, 20157) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1784, 4438, 20157 is 1.
Step 1: Since 4438 > 1784, we apply the division lemma to 4438 and 1784, to get
4438 = 1784 x 2 + 870
Step 2: Since the reminder 1784 ≠ 0, we apply division lemma to 870 and 1784, to get
1784 = 870 x 2 + 44
Step 3: We consider the new divisor 870 and the new remainder 44, and apply the division lemma to get
870 = 44 x 19 + 34
We consider the new divisor 44 and the new remainder 34,and apply the division lemma to get
44 = 34 x 1 + 10
We consider the new divisor 34 and the new remainder 10,and apply the division lemma to get
34 = 10 x 3 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1784 and 4438 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(34,10) = HCF(44,34) = HCF(870,44) = HCF(1784,870) = HCF(4438,1784) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 20157 > 2, we apply the division lemma to 20157 and 2, to get
20157 = 2 x 10078 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 20157 is 1
Notice that 1 = HCF(2,1) = HCF(20157,2) .
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 1784, 4438, 20157?
Answer: HCF of 1784, 4438, 20157 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1784, 4438, 20157 using Euclid's Algorithm?
Answer: For arbitrary numbers 1784, 4438, 20157 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.