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 2669, 643 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2669, 643 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 2669, 643 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 2669, 643 is 1.
HCF(2669, 643) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2669, 643 is 1.
Step 1: Since 2669 > 643, we apply the division lemma to 2669 and 643, to get
2669 = 643 x 4 + 97
Step 2: Since the reminder 643 ≠ 0, we apply division lemma to 97 and 643, to get
643 = 97 x 6 + 61
Step 3: We consider the new divisor 97 and the new remainder 61, and apply the division lemma to get
97 = 61 x 1 + 36
We consider the new divisor 61 and the new remainder 36,and apply the division lemma to get
61 = 36 x 1 + 25
We consider the new divisor 36 and the new remainder 25,and apply the division lemma to get
36 = 25 x 1 + 11
We consider the new divisor 25 and the new remainder 11,and apply the division lemma to get
25 = 11 x 2 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 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 2669 and 643 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(25,11) = HCF(36,25) = HCF(61,36) = HCF(97,61) = HCF(643,97) = HCF(2669,643) .
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 2669, 643?
Answer: HCF of 2669, 643 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2669, 643 using Euclid's Algorithm?
Answer: For arbitrary numbers 2669, 643 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.