Highest Common Factor of 963, 21045 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 963, 21045 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 963, 21045 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 963, 21045 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 963, 21045 is 3.
HCF(963, 21045) = 3
HCF of 963, 21045 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 963, 21045 is 3.
Highest Common Factor of 963,21045 is 3
Step 1: Since 21045 > 963, we apply the division lemma to 21045 and 963, to get
21045 = 963 x 21 + 822
Step 2: Since the reminder 963 ≠ 0, we apply division lemma to 822 and 963, to get
963 = 822 x 1 + 141
Step 3: We consider the new divisor 822 and the new remainder 141, and apply the division lemma to get
822 = 141 x 5 + 117
We consider the new divisor 141 and the new remainder 117,and apply the division lemma to get
141 = 117 x 1 + 24
We consider the new divisor 117 and the new remainder 24,and apply the division lemma to get
117 = 24 x 4 + 21
We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get
24 = 21 x 1 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 963 and 21045 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(117,24) = HCF(141,117) = HCF(822,141) = HCF(963,822) = HCF(21045,963) .
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Frequently Asked Questions on HCF of 963, 21045 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 963, 21045?
Answer: HCF of 963, 21045 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 963, 21045 using Euclid's Algorithm?
Answer: For arbitrary numbers 963, 21045 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.