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 513, 867, 17 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 513, 867, 17 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 513, 867, 17 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 513, 867, 17 is 1.
HCF(513, 867, 17) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 513, 867, 17 is 1.
Step 1: Since 867 > 513, we apply the division lemma to 867 and 513, to get
867 = 513 x 1 + 354
Step 2: Since the reminder 513 ≠ 0, we apply division lemma to 354 and 513, to get
513 = 354 x 1 + 159
Step 3: We consider the new divisor 354 and the new remainder 159, and apply the division lemma to get
354 = 159 x 2 + 36
We consider the new divisor 159 and the new remainder 36,and apply the division lemma to get
159 = 36 x 4 + 15
We consider the new divisor 36 and the new remainder 15,and apply the division lemma to get
36 = 15 x 2 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 513 and 867 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(36,15) = HCF(159,36) = HCF(354,159) = HCF(513,354) = HCF(867,513) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 17 > 3, we apply the division lemma to 17 and 3, to get
17 = 3 x 5 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 17 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(17,3) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 513, 867, 17?
Answer: HCF of 513, 867, 17 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 513, 867, 17 using Euclid's Algorithm?
Answer: For arbitrary numbers 513, 867, 17 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.