Highest Common Factor of 9696, 9908 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 9696, 9908 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 9696, 9908 is 4 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 9696, 9908 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 9696, 9908 is 4.
HCF(9696, 9908) = 4
HCF of 9696, 9908 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9696, 9908 is 4.
Highest Common Factor of 9696,9908 is 4
Step 1: Since 9908 > 9696, we apply the division lemma to 9908 and 9696, to get
9908 = 9696 x 1 + 212
Step 2: Since the reminder 9696 ≠ 0, we apply division lemma to 212 and 9696, to get
9696 = 212 x 45 + 156
Step 3: We consider the new divisor 212 and the new remainder 156, and apply the division lemma to get
212 = 156 x 1 + 56
We consider the new divisor 156 and the new remainder 56,and apply the division lemma to get
156 = 56 x 2 + 44
We consider the new divisor 56 and the new remainder 44,and apply the division lemma to get
56 = 44 x 1 + 12
We consider the new divisor 44 and the new remainder 12,and apply the division lemma to get
44 = 12 x 3 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 9696 and 9908 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(44,12) = HCF(56,44) = HCF(156,56) = HCF(212,156) = HCF(9696,212) = HCF(9908,9696) .
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Frequently Asked Questions on HCF of 9696, 9908 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 9696, 9908?
Answer: HCF of 9696, 9908 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9696, 9908 using Euclid's Algorithm?
Answer: For arbitrary numbers 9696, 9908 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.