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 9706, 7981 i.e. 23 the largest integer that leaves a remainder zero for all numbers.
HCF of 9706, 7981 is 23 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 9706, 7981 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 9706, 7981 is 23.
HCF(9706, 7981) = 23
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9706, 7981 is 23.
Step 1: Since 9706 > 7981, we apply the division lemma to 9706 and 7981, to get
9706 = 7981 x 1 + 1725
Step 2: Since the reminder 7981 ≠ 0, we apply division lemma to 1725 and 7981, to get
7981 = 1725 x 4 + 1081
Step 3: We consider the new divisor 1725 and the new remainder 1081, and apply the division lemma to get
1725 = 1081 x 1 + 644
We consider the new divisor 1081 and the new remainder 644,and apply the division lemma to get
1081 = 644 x 1 + 437
We consider the new divisor 644 and the new remainder 437,and apply the division lemma to get
644 = 437 x 1 + 207
We consider the new divisor 437 and the new remainder 207,and apply the division lemma to get
437 = 207 x 2 + 23
We consider the new divisor 207 and the new remainder 23,and apply the division lemma to get
207 = 23 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 23, the HCF of 9706 and 7981 is 23
Notice that 23 = HCF(207,23) = HCF(437,207) = HCF(644,437) = HCF(1081,644) = HCF(1725,1081) = HCF(7981,1725) = HCF(9706,7981) .
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 9706, 7981?
Answer: HCF of 9706, 7981 is 23 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9706, 7981 using Euclid's Algorithm?
Answer: For arbitrary numbers 9706, 7981 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.