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 8698, 9996 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8698, 9996 is 2 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 8698, 9996 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 8698, 9996 is 2.
HCF(8698, 9996) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8698, 9996 is 2.
Step 1: Since 9996 > 8698, we apply the division lemma to 9996 and 8698, to get
9996 = 8698 x 1 + 1298
Step 2: Since the reminder 8698 ≠ 0, we apply division lemma to 1298 and 8698, to get
8698 = 1298 x 6 + 910
Step 3: We consider the new divisor 1298 and the new remainder 910, and apply the division lemma to get
1298 = 910 x 1 + 388
We consider the new divisor 910 and the new remainder 388,and apply the division lemma to get
910 = 388 x 2 + 134
We consider the new divisor 388 and the new remainder 134,and apply the division lemma to get
388 = 134 x 2 + 120
We consider the new divisor 134 and the new remainder 120,and apply the division lemma to get
134 = 120 x 1 + 14
We consider the new divisor 120 and the new remainder 14,and apply the division lemma to get
120 = 14 x 8 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8698 and 9996 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(120,14) = HCF(134,120) = HCF(388,134) = HCF(910,388) = HCF(1298,910) = HCF(8698,1298) = HCF(9996,8698) .
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 8698, 9996?
Answer: HCF of 8698, 9996 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8698, 9996 using Euclid's Algorithm?
Answer: For arbitrary numbers 8698, 9996 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.