Highest Common Factor of 9888, 8110 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 9888, 8110 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 9888, 8110 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 9888, 8110 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 9888, 8110 is 2.
HCF(9888, 8110) = 2
HCF of 9888, 8110 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9888, 8110 is 2.
Highest Common Factor of 9888,8110 is 2
Step 1: Since 9888 > 8110, we apply the division lemma to 9888 and 8110, to get
9888 = 8110 x 1 + 1778
Step 2: Since the reminder 8110 ≠ 0, we apply division lemma to 1778 and 8110, to get
8110 = 1778 x 4 + 998
Step 3: We consider the new divisor 1778 and the new remainder 998, and apply the division lemma to get
1778 = 998 x 1 + 780
We consider the new divisor 998 and the new remainder 780,and apply the division lemma to get
998 = 780 x 1 + 218
We consider the new divisor 780 and the new remainder 218,and apply the division lemma to get
780 = 218 x 3 + 126
We consider the new divisor 218 and the new remainder 126,and apply the division lemma to get
218 = 126 x 1 + 92
We consider the new divisor 126 and the new remainder 92,and apply the division lemma to get
126 = 92 x 1 + 34
We consider the new divisor 92 and the new remainder 34,and apply the division lemma to get
92 = 34 x 2 + 24
We consider the new divisor 34 and the new remainder 24,and apply the division lemma to get
34 = 24 x 1 + 10
We consider the new divisor 24 and the new remainder 10,and apply the division lemma to get
24 = 10 x 2 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 9888 and 8110 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(24,10) = HCF(34,24) = HCF(92,34) = HCF(126,92) = HCF(218,126) = HCF(780,218) = HCF(998,780) = HCF(1778,998) = HCF(8110,1778) = HCF(9888,8110) .
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Frequently Asked Questions on HCF of 9888, 8110 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 9888, 8110?
Answer: HCF of 9888, 8110 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9888, 8110 using Euclid's Algorithm?
Answer: For arbitrary numbers 9888, 8110 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.