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 743, 455, 629 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 743, 455, 629 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 743, 455, 629 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 743, 455, 629 is 1.
HCF(743, 455, 629) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 743, 455, 629 is 1.
Step 1: Since 743 > 455, we apply the division lemma to 743 and 455, to get
743 = 455 x 1 + 288
Step 2: Since the reminder 455 ≠ 0, we apply division lemma to 288 and 455, to get
455 = 288 x 1 + 167
Step 3: We consider the new divisor 288 and the new remainder 167, and apply the division lemma to get
288 = 167 x 1 + 121
We consider the new divisor 167 and the new remainder 121,and apply the division lemma to get
167 = 121 x 1 + 46
We consider the new divisor 121 and the new remainder 46,and apply the division lemma to get
121 = 46 x 2 + 29
We consider the new divisor 46 and the new remainder 29,and apply the division lemma to get
46 = 29 x 1 + 17
We consider the new divisor 29 and the new remainder 17,and apply the division lemma to get
29 = 17 x 1 + 12
We consider the new divisor 17 and the new remainder 12,and apply the division lemma to get
17 = 12 x 1 + 5
We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get
12 = 5 x 2 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 743 and 455 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(17,12) = HCF(29,17) = HCF(46,29) = HCF(121,46) = HCF(167,121) = HCF(288,167) = HCF(455,288) = HCF(743,455) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 629 > 1, we apply the division lemma to 629 and 1, to get
629 = 1 x 629 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 629 is 1
Notice that 1 = HCF(629,1) .
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 743, 455, 629?
Answer: HCF of 743, 455, 629 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 743, 455, 629 using Euclid's Algorithm?
Answer: For arbitrary numbers 743, 455, 629 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.