Highest Common Factor of 1026, 7688, 29832 using Euclid's algorithm
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 1026, 7688, 29832 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1026, 7688, 29832 is 2 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 1026, 7688, 29832 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 1026, 7688, 29832 is 2.
HCF(1026, 7688, 29832) = 2
HCF of 1026, 7688, 29832 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1026, 7688, 29832 is 2.
Highest Common Factor of 1026,7688,29832 is 2
Step 1: Since 7688 > 1026, we apply the division lemma to 7688 and 1026, to get
7688 = 1026 x 7 + 506
Step 2: Since the reminder 1026 ≠ 0, we apply division lemma to 506 and 1026, to get
1026 = 506 x 2 + 14
Step 3: We consider the new divisor 506 and the new remainder 14, and apply the division lemma to get
506 = 14 x 36 + 2
We consider the new divisor 14 and the new remainder 2, and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1026 and 7688 is 2
Notice that 2 = HCF(14,2) = HCF(506,14) = HCF(1026,506) = HCF(7688,1026) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 29832 > 2, we apply the division lemma to 29832 and 2, to get
29832 = 2 x 14916 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 29832 is 2
Notice that 2 = HCF(29832,2) .
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Frequently Asked Questions on HCF of 1026, 7688, 29832 using Euclid's Algorithm
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 1026, 7688, 29832?
Answer: HCF of 1026, 7688, 29832 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1026, 7688, 29832 using Euclid's Algorithm?
Answer: For arbitrary numbers 1026, 7688, 29832 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.