Highest Common Factor of 643, 470, 663 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 643, 470, 663 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 643, 470, 663 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 643, 470, 663 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 643, 470, 663 is 1.
HCF(643, 470, 663) = 1
HCF of 643, 470, 663 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 643, 470, 663 is 1.
Highest Common Factor of 643,470,663 is 1
Step 1: Since 643 > 470, we apply the division lemma to 643 and 470, to get
643 = 470 x 1 + 173
Step 2: Since the reminder 470 ≠ 0, we apply division lemma to 173 and 470, to get
470 = 173 x 2 + 124
Step 3: We consider the new divisor 173 and the new remainder 124, and apply the division lemma to get
173 = 124 x 1 + 49
We consider the new divisor 124 and the new remainder 49,and apply the division lemma to get
124 = 49 x 2 + 26
We consider the new divisor 49 and the new remainder 26,and apply the division lemma to get
49 = 26 x 1 + 23
We consider the new divisor 26 and the new remainder 23,and apply the division lemma to get
26 = 23 x 1 + 3
We consider the new divisor 23 and the new remainder 3,and apply the division lemma to get
23 = 3 x 7 + 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 643 and 470 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(23,3) = HCF(26,23) = HCF(49,26) = HCF(124,49) = HCF(173,124) = HCF(470,173) = HCF(643,470) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 663 > 1, we apply the division lemma to 663 and 1, to get
663 = 1 x 663 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 663 is 1
Notice that 1 = HCF(663,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 643, 470, 663 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 643, 470, 663?
Answer: HCF of 643, 470, 663 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 643, 470, 663 using Euclid's Algorithm?
Answer: For arbitrary numbers 643, 470, 663 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
