Highest Common Factor of 9772, 3638 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 9772, 3638 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 9772, 3638 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 9772, 3638 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 9772, 3638 is 2.
HCF(9772, 3638) = 2
HCF of 9772, 3638 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9772, 3638 is 2.
Highest Common Factor of 9772,3638 is 2
Step 1: Since 9772 > 3638, we apply the division lemma to 9772 and 3638, to get
9772 = 3638 x 2 + 2496
Step 2: Since the reminder 3638 ≠ 0, we apply division lemma to 2496 and 3638, to get
3638 = 2496 x 1 + 1142
Step 3: We consider the new divisor 2496 and the new remainder 1142, and apply the division lemma to get
2496 = 1142 x 2 + 212
We consider the new divisor 1142 and the new remainder 212,and apply the division lemma to get
1142 = 212 x 5 + 82
We consider the new divisor 212 and the new remainder 82,and apply the division lemma to get
212 = 82 x 2 + 48
We consider the new divisor 82 and the new remainder 48,and apply the division lemma to get
82 = 48 x 1 + 34
We consider the new divisor 48 and the new remainder 34,and apply the division lemma to get
48 = 34 x 1 + 14
We consider the new divisor 34 and the new remainder 14,and apply the division lemma to get
34 = 14 x 2 + 6
We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get
14 = 6 x 2 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 9772 and 3638 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(34,14) = HCF(48,34) = HCF(82,48) = HCF(212,82) = HCF(1142,212) = HCF(2496,1142) = HCF(3638,2496) = HCF(9772,3638) .
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Frequently Asked Questions on HCF of 9772, 3638 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 9772, 3638?
Answer: HCF of 9772, 3638 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9772, 3638 using Euclid's Algorithm?
Answer: For arbitrary numbers 9772, 3638 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.