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 9996, 9823 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9996, 9823 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 9996, 9823 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 9996, 9823 is 1.
HCF(9996, 9823) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9996, 9823 is 1.
Step 1: Since 9996 > 9823, we apply the division lemma to 9996 and 9823, to get
9996 = 9823 x 1 + 173
Step 2: Since the reminder 9823 ≠ 0, we apply division lemma to 173 and 9823, to get
9823 = 173 x 56 + 135
Step 3: We consider the new divisor 173 and the new remainder 135, and apply the division lemma to get
173 = 135 x 1 + 38
We consider the new divisor 135 and the new remainder 38,and apply the division lemma to get
135 = 38 x 3 + 21
We consider the new divisor 38 and the new remainder 21,and apply the division lemma to get
38 = 21 x 1 + 17
We consider the new divisor 21 and the new remainder 17,and apply the division lemma to get
21 = 17 x 1 + 4
We consider the new divisor 17 and the new remainder 4,and apply the division lemma to get
17 = 4 x 4 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9996 and 9823 is 1
Notice that 1 = HCF(4,1) = HCF(17,4) = HCF(21,17) = HCF(38,21) = HCF(135,38) = HCF(173,135) = HCF(9823,173) = HCF(9996,9823) .
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 9996, 9823?
Answer: HCF of 9996, 9823 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9996, 9823 using Euclid's Algorithm?
Answer: For arbitrary numbers 9996, 9823 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.