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 829, 642, 19 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 829, 642, 19 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 829, 642, 19 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 829, 642, 19 is 1.
HCF(829, 642, 19) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 829, 642, 19 is 1.
Step 1: Since 829 > 642, we apply the division lemma to 829 and 642, to get
829 = 642 x 1 + 187
Step 2: Since the reminder 642 ≠ 0, we apply division lemma to 187 and 642, to get
642 = 187 x 3 + 81
Step 3: We consider the new divisor 187 and the new remainder 81, and apply the division lemma to get
187 = 81 x 2 + 25
We consider the new divisor 81 and the new remainder 25,and apply the division lemma to get
81 = 25 x 3 + 6
We consider the new divisor 25 and the new remainder 6,and apply the division lemma to get
25 = 6 x 4 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 829 and 642 is 1
Notice that 1 = HCF(6,1) = HCF(25,6) = HCF(81,25) = HCF(187,81) = HCF(642,187) = HCF(829,642) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 19 > 1, we apply the division lemma to 19 and 1, to get
19 = 1 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 19 is 1
Notice that 1 = HCF(19,1) .
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 829, 642, 19?
Answer: HCF of 829, 642, 19 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 829, 642, 19 using Euclid's Algorithm?
Answer: For arbitrary numbers 829, 642, 19 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.