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 419, 3505, 2829 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 419, 3505, 2829 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 419, 3505, 2829 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 419, 3505, 2829 is 1.
HCF(419, 3505, 2829) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 419, 3505, 2829 is 1.
Step 1: Since 3505 > 419, we apply the division lemma to 3505 and 419, to get
3505 = 419 x 8 + 153
Step 2: Since the reminder 419 ≠ 0, we apply division lemma to 153 and 419, to get
419 = 153 x 2 + 113
Step 3: We consider the new divisor 153 and the new remainder 113, and apply the division lemma to get
153 = 113 x 1 + 40
We consider the new divisor 113 and the new remainder 40,and apply the division lemma to get
113 = 40 x 2 + 33
We consider the new divisor 40 and the new remainder 33,and apply the division lemma to get
40 = 33 x 1 + 7
We consider the new divisor 33 and the new remainder 7,and apply the division lemma to get
33 = 7 x 4 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 419 and 3505 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(33,7) = HCF(40,33) = HCF(113,40) = HCF(153,113) = HCF(419,153) = HCF(3505,419) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2829 > 1, we apply the division lemma to 2829 and 1, to get
2829 = 1 x 2829 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 2829 is 1
Notice that 1 = HCF(2829,1) .
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 419, 3505, 2829?
Answer: HCF of 419, 3505, 2829 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 419, 3505, 2829 using Euclid's Algorithm?
Answer: For arbitrary numbers 419, 3505, 2829 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.