Highest Common Factor of 9969, 1629 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 9969, 1629 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 9969, 1629 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 9969, 1629 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 9969, 1629 is 3.
HCF(9969, 1629) = 3
HCF of 9969, 1629 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9969, 1629 is 3.
Highest Common Factor of 9969,1629 is 3
Step 1: Since 9969 > 1629, we apply the division lemma to 9969 and 1629, to get
9969 = 1629 x 6 + 195
Step 2: Since the reminder 1629 ≠ 0, we apply division lemma to 195 and 1629, to get
1629 = 195 x 8 + 69
Step 3: We consider the new divisor 195 and the new remainder 69, and apply the division lemma to get
195 = 69 x 2 + 57
We consider the new divisor 69 and the new remainder 57,and apply the division lemma to get
69 = 57 x 1 + 12
We consider the new divisor 57 and the new remainder 12,and apply the division lemma to get
57 = 12 x 4 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9969 and 1629 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(57,12) = HCF(69,57) = HCF(195,69) = HCF(1629,195) = HCF(9969,1629) .
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Frequently Asked Questions on HCF of 9969, 1629 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 9969, 1629?
Answer: HCF of 9969, 1629 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9969, 1629 using Euclid's Algorithm?
Answer: For arbitrary numbers 9969, 1629 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.