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 5830, 8938, 61743 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 5830, 8938, 61743 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 5830, 8938, 61743 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 5830, 8938, 61743 is 1.
HCF(5830, 8938, 61743) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5830, 8938, 61743 is 1.
Step 1: Since 8938 > 5830, we apply the division lemma to 8938 and 5830, to get
8938 = 5830 x 1 + 3108
Step 2: Since the reminder 5830 ≠ 0, we apply division lemma to 3108 and 5830, to get
5830 = 3108 x 1 + 2722
Step 3: We consider the new divisor 3108 and the new remainder 2722, and apply the division lemma to get
3108 = 2722 x 1 + 386
We consider the new divisor 2722 and the new remainder 386,and apply the division lemma to get
2722 = 386 x 7 + 20
We consider the new divisor 386 and the new remainder 20,and apply the division lemma to get
386 = 20 x 19 + 6
We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get
20 = 6 x 3 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 5830 and 8938 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(386,20) = HCF(2722,386) = HCF(3108,2722) = HCF(5830,3108) = HCF(8938,5830) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 61743 > 2, we apply the division lemma to 61743 and 2, to get
61743 = 2 x 30871 + 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 61743 is 1
Notice that 1 = HCF(2,1) = HCF(61743,2) .
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 5830, 8938, 61743?
Answer: HCF of 5830, 8938, 61743 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5830, 8938, 61743 using Euclid's Algorithm?
Answer: For arbitrary numbers 5830, 8938, 61743 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.