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 691, 2582 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 691, 2582 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 691, 2582 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 691, 2582 is 1.
HCF(691, 2582) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 691, 2582 is 1.
Step 1: Since 2582 > 691, we apply the division lemma to 2582 and 691, to get
2582 = 691 x 3 + 509
Step 2: Since the reminder 691 ≠ 0, we apply division lemma to 509 and 691, to get
691 = 509 x 1 + 182
Step 3: We consider the new divisor 509 and the new remainder 182, and apply the division lemma to get
509 = 182 x 2 + 145
We consider the new divisor 182 and the new remainder 145,and apply the division lemma to get
182 = 145 x 1 + 37
We consider the new divisor 145 and the new remainder 37,and apply the division lemma to get
145 = 37 x 3 + 34
We consider the new divisor 37 and the new remainder 34,and apply the division lemma to get
37 = 34 x 1 + 3
We consider the new divisor 34 and the new remainder 3,and apply the division lemma to get
34 = 3 x 11 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 691 and 2582 is 1
Notice that 1 = HCF(3,1) = HCF(34,3) = HCF(37,34) = HCF(145,37) = HCF(182,145) = HCF(509,182) = HCF(691,509) = HCF(2582,691) .
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 691, 2582?
Answer: HCF of 691, 2582 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 691, 2582 using Euclid's Algorithm?
Answer: For arbitrary numbers 691, 2582 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.