Highest Common Factor of 1538, 6585 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 1538, 6585 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1538, 6585 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 1538, 6585 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 1538, 6585 is 1.
HCF(1538, 6585) = 1
HCF of 1538, 6585 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1538, 6585 is 1.
Highest Common Factor of 1538,6585 is 1
Step 1: Since 6585 > 1538, we apply the division lemma to 6585 and 1538, to get
6585 = 1538 x 4 + 433
Step 2: Since the reminder 1538 ≠ 0, we apply division lemma to 433 and 1538, to get
1538 = 433 x 3 + 239
Step 3: We consider the new divisor 433 and the new remainder 239, and apply the division lemma to get
433 = 239 x 1 + 194
We consider the new divisor 239 and the new remainder 194,and apply the division lemma to get
239 = 194 x 1 + 45
We consider the new divisor 194 and the new remainder 45,and apply the division lemma to get
194 = 45 x 4 + 14
We consider the new divisor 45 and the new remainder 14,and apply the division lemma to get
45 = 14 x 3 + 3
We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get
14 = 3 x 4 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 1538 and 6585 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(45,14) = HCF(194,45) = HCF(239,194) = HCF(433,239) = HCF(1538,433) = HCF(6585,1538) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 1538, 6585 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 1538, 6585?
Answer: HCF of 1538, 6585 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1538, 6585 using Euclid's Algorithm?
Answer: For arbitrary numbers 1538, 6585 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.