Highest Common Factor of 9688, 3112 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 9688, 3112 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 9688, 3112 is 8 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 9688, 3112 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 9688, 3112 is 8.
HCF(9688, 3112) = 8
HCF of 9688, 3112 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9688, 3112 is 8.
Highest Common Factor of 9688,3112 is 8
Step 1: Since 9688 > 3112, we apply the division lemma to 9688 and 3112, to get
9688 = 3112 x 3 + 352
Step 2: Since the reminder 3112 ≠ 0, we apply division lemma to 352 and 3112, to get
3112 = 352 x 8 + 296
Step 3: We consider the new divisor 352 and the new remainder 296, and apply the division lemma to get
352 = 296 x 1 + 56
We consider the new divisor 296 and the new remainder 56,and apply the division lemma to get
296 = 56 x 5 + 16
We consider the new divisor 56 and the new remainder 16,and apply the division lemma to get
56 = 16 x 3 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 9688 and 3112 is 8
Notice that 8 = HCF(16,8) = HCF(56,16) = HCF(296,56) = HCF(352,296) = HCF(3112,352) = HCF(9688,3112) .
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Frequently Asked Questions on HCF of 9688, 3112 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 9688, 3112?
Answer: HCF of 9688, 3112 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9688, 3112 using Euclid's Algorithm?
Answer: For arbitrary numbers 9688, 3112 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.