Highest Common Factor of 9696, 9945 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, 9945 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 9696, 9945 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 9696, 9945 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, 9945 is 3.
HCF(9696, 9945) = 3
HCF of 9696, 9945 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, 9945 is 3.
Highest Common Factor of 9696,9945 is 3
Step 1: Since 9945 > 9696, we apply the division lemma to 9945 and 9696, to get
9945 = 9696 x 1 + 249
Step 2: Since the reminder 9696 ≠ 0, we apply division lemma to 249 and 9696, to get
9696 = 249 x 38 + 234
Step 3: We consider the new divisor 249 and the new remainder 234, and apply the division lemma to get
249 = 234 x 1 + 15
We consider the new divisor 234 and the new remainder 15,and apply the division lemma to get
234 = 15 x 15 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 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 9696 and 9945 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(234,15) = HCF(249,234) = HCF(9696,249) = HCF(9945,9696) .
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Frequently Asked Questions on HCF of 9696, 9945 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, 9945?
Answer: HCF of 9696, 9945 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9696, 9945 using Euclid's Algorithm?
Answer: For arbitrary numbers 9696, 9945 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.