Highest Common Factor of 117, 9729 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 117, 9729 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 117, 9729 is 9 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 117, 9729 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 117, 9729 is 9.
HCF(117, 9729) = 9
HCF of 117, 9729 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 117, 9729 is 9.
Highest Common Factor of 117,9729 is 9
Step 1: Since 9729 > 117, we apply the division lemma to 9729 and 117, to get
9729 = 117 x 83 + 18
Step 2: Since the reminder 117 ≠ 0, we apply division lemma to 18 and 117, to get
117 = 18 x 6 + 9
Step 3: We consider the new divisor 18 and the new remainder 9, and apply the division lemma to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 117 and 9729 is 9
Notice that 9 = HCF(18,9) = HCF(117,18) = HCF(9729,117) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 117, 9729 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 117, 9729?
Answer: HCF of 117, 9729 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 117, 9729 using Euclid's Algorithm?
Answer: For arbitrary numbers 117, 9729 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.