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 8520, 9723 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 8520, 9723 is 3 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 8520, 9723 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 8520, 9723 is 3.
HCF(8520, 9723) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8520, 9723 is 3.
Step 1: Since 9723 > 8520, we apply the division lemma to 9723 and 8520, to get
9723 = 8520 x 1 + 1203
Step 2: Since the reminder 8520 ≠ 0, we apply division lemma to 1203 and 8520, to get
8520 = 1203 x 7 + 99
Step 3: We consider the new divisor 1203 and the new remainder 99, and apply the division lemma to get
1203 = 99 x 12 + 15
We consider the new divisor 99 and the new remainder 15,and apply the division lemma to get
99 = 15 x 6 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 8520 and 9723 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(99,15) = HCF(1203,99) = HCF(8520,1203) = HCF(9723,8520) .
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 8520, 9723?
Answer: HCF of 8520, 9723 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8520, 9723 using Euclid's Algorithm?
Answer: For arbitrary numbers 8520, 9723 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.