Highest Common Factor of 963, 356, 513 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, 356, 513 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 963, 356, 513 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 963, 356, 513 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, 356, 513 is 1.
HCF(963, 356, 513) = 1
HCF of 963, 356, 513 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, 356, 513 is 1.
Highest Common Factor of 963,356,513 is 1
Step 1: Since 963 > 356, we apply the division lemma to 963 and 356, to get
963 = 356 x 2 + 251
Step 2: Since the reminder 356 ≠ 0, we apply division lemma to 251 and 356, to get
356 = 251 x 1 + 105
Step 3: We consider the new divisor 251 and the new remainder 105, and apply the division lemma to get
251 = 105 x 2 + 41
We consider the new divisor 105 and the new remainder 41,and apply the division lemma to get
105 = 41 x 2 + 23
We consider the new divisor 41 and the new remainder 23,and apply the division lemma to get
41 = 23 x 1 + 18
We consider the new divisor 23 and the new remainder 18,and apply the division lemma to get
23 = 18 x 1 + 5
We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get
18 = 5 x 3 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 963 and 356 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(23,18) = HCF(41,23) = HCF(105,41) = HCF(251,105) = HCF(356,251) = HCF(963,356) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 513 > 1, we apply the division lemma to 513 and 1, to get
513 = 1 x 513 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 513 is 1
Notice that 1 = HCF(513,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 963, 356, 513 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, 356, 513?
Answer: HCF of 963, 356, 513 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 963, 356, 513 using Euclid's Algorithm?
Answer: For arbitrary numbers 963, 356, 513 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
