Highest Common Factor of 1712, 2369 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 1712, 2369 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1712, 2369 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 1712, 2369 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 1712, 2369 is 1.
HCF(1712, 2369) = 1
HCF of 1712, 2369 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1712, 2369 is 1.
Highest Common Factor of 1712,2369 is 1
Step 1: Since 2369 > 1712, we apply the division lemma to 2369 and 1712, to get
2369 = 1712 x 1 + 657
Step 2: Since the reminder 1712 ≠ 0, we apply division lemma to 657 and 1712, to get
1712 = 657 x 2 + 398
Step 3: We consider the new divisor 657 and the new remainder 398, and apply the division lemma to get
657 = 398 x 1 + 259
We consider the new divisor 398 and the new remainder 259,and apply the division lemma to get
398 = 259 x 1 + 139
We consider the new divisor 259 and the new remainder 139,and apply the division lemma to get
259 = 139 x 1 + 120
We consider the new divisor 139 and the new remainder 120,and apply the division lemma to get
139 = 120 x 1 + 19
We consider the new divisor 120 and the new remainder 19,and apply the division lemma to get
120 = 19 x 6 + 6
We consider the new divisor 19 and the new remainder 6,and apply the division lemma to get
19 = 6 x 3 + 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 1712 and 2369 is 1
Notice that 1 = HCF(6,1) = HCF(19,6) = HCF(120,19) = HCF(139,120) = HCF(259,139) = HCF(398,259) = HCF(657,398) = HCF(1712,657) = HCF(2369,1712) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 1712, 2369 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 1712, 2369?
Answer: HCF of 1712, 2369 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1712, 2369 using Euclid's Algorithm?
Answer: For arbitrary numbers 1712, 2369 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.