Highest Common Factor of 163, 9825, 9635 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 163, 9825, 9635 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 163, 9825, 9635 is 1 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 163, 9825, 9635 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 163, 9825, 9635 is 1.
HCF(163, 9825, 9635) = 1
HCF of 163, 9825, 9635 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 163, 9825, 9635 is 1.
Highest Common Factor of 163,9825,9635 is 1
Step 1: Since 9825 > 163, we apply the division lemma to 9825 and 163, to get
9825 = 163 x 60 + 45
Step 2: Since the reminder 163 ≠ 0, we apply division lemma to 45 and 163, to get
163 = 45 x 3 + 28
Step 3: We consider the new divisor 45 and the new remainder 28, and apply the division lemma to get
45 = 28 x 1 + 17
We consider the new divisor 28 and the new remainder 17,and apply the division lemma to get
28 = 17 x 1 + 11
We consider the new divisor 17 and the new remainder 11,and apply the division lemma to get
17 = 11 x 1 + 6
We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get
11 = 6 x 1 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 163 and 9825 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(17,11) = HCF(28,17) = HCF(45,28) = HCF(163,45) = HCF(9825,163) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9635 > 1, we apply the division lemma to 9635 and 1, to get
9635 = 1 x 9635 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 9635 is 1
Notice that 1 = HCF(9635,1) .
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Frequently Asked Questions on HCF of 163, 9825, 9635 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 163, 9825, 9635?
Answer: HCF of 163, 9825, 9635 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 163, 9825, 9635 using Euclid's Algorithm?
Answer: For arbitrary numbers 163, 9825, 9635 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.