Highest Common Factor of 419, 720, 287 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 419, 720, 287 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 419, 720, 287 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, 720, 287 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, 720, 287 is 1.
HCF(419, 720, 287) = 1
HCF of 419, 720, 287 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 419, 720, 287 is 1.
Highest Common Factor of 419,720,287 is 1
Step 1: Since 720 > 419, we apply the division lemma to 720 and 419, to get
720 = 419 x 1 + 301
Step 2: Since the reminder 419 ≠ 0, we apply division lemma to 301 and 419, to get
419 = 301 x 1 + 118
Step 3: We consider the new divisor 301 and the new remainder 118, and apply the division lemma to get
301 = 118 x 2 + 65
We consider the new divisor 118 and the new remainder 65,and apply the division lemma to get
118 = 65 x 1 + 53
We consider the new divisor 65 and the new remainder 53,and apply the division lemma to get
65 = 53 x 1 + 12
We consider the new divisor 53 and the new remainder 12,and apply the division lemma to get
53 = 12 x 4 + 5
We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get
12 = 5 x 2 + 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 720 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(53,12) = HCF(65,53) = HCF(118,65) = HCF(301,118) = HCF(419,301) = HCF(720,419) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 287 > 1, we apply the division lemma to 287 and 1, to get
287 = 1 x 287 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 287 is 1
Notice that 1 = HCF(287,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 419, 720, 287 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 419, 720, 287?
Answer: HCF of 419, 720, 287 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 419, 720, 287 using Euclid's Algorithm?
Answer: For arbitrary numbers 419, 720, 287 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.