Highest Common Factor of 8997, 8157 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 8997, 8157 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 8997, 8157 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 8997, 8157 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 8997, 8157 is 3.
HCF(8997, 8157) = 3
HCF of 8997, 8157 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8997, 8157 is 3.
Highest Common Factor of 8997,8157 is 3
Step 1: Since 8997 > 8157, we apply the division lemma to 8997 and 8157, to get
8997 = 8157 x 1 + 840
Step 2: Since the reminder 8157 ≠ 0, we apply division lemma to 840 and 8157, to get
8157 = 840 x 9 + 597
Step 3: We consider the new divisor 840 and the new remainder 597, and apply the division lemma to get
840 = 597 x 1 + 243
We consider the new divisor 597 and the new remainder 243,and apply the division lemma to get
597 = 243 x 2 + 111
We consider the new divisor 243 and the new remainder 111,and apply the division lemma to get
243 = 111 x 2 + 21
We consider the new divisor 111 and the new remainder 21,and apply the division lemma to get
111 = 21 x 5 + 6
We consider the new divisor 21 and the new remainder 6,and apply the division lemma to get
21 = 6 x 3 + 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 8997 and 8157 is 3
Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(111,21) = HCF(243,111) = HCF(597,243) = HCF(840,597) = HCF(8157,840) = HCF(8997,8157) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 8997, 8157 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 8997, 8157?
Answer: HCF of 8997, 8157 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8997, 8157 using Euclid's Algorithm?
Answer: For arbitrary numbers 8997, 8157 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.