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 723, 443, 476 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 723, 443, 476 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 723, 443, 476 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 723, 443, 476 is 1.
HCF(723, 443, 476) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 723, 443, 476 is 1.
Step 1: Since 723 > 443, we apply the division lemma to 723 and 443, to get
723 = 443 x 1 + 280
Step 2: Since the reminder 443 ≠ 0, we apply division lemma to 280 and 443, to get
443 = 280 x 1 + 163
Step 3: We consider the new divisor 280 and the new remainder 163, and apply the division lemma to get
280 = 163 x 1 + 117
We consider the new divisor 163 and the new remainder 117,and apply the division lemma to get
163 = 117 x 1 + 46
We consider the new divisor 117 and the new remainder 46,and apply the division lemma to get
117 = 46 x 2 + 25
We consider the new divisor 46 and the new remainder 25,and apply the division lemma to get
46 = 25 x 1 + 21
We consider the new divisor 25 and the new remainder 21,and apply the division lemma to get
25 = 21 x 1 + 4
We consider the new divisor 21 and the new remainder 4,and apply the division lemma to get
21 = 4 x 5 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 723 and 443 is 1
Notice that 1 = HCF(4,1) = HCF(21,4) = HCF(25,21) = HCF(46,25) = HCF(117,46) = HCF(163,117) = HCF(280,163) = HCF(443,280) = HCF(723,443) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 476 > 1, we apply the division lemma to 476 and 1, to get
476 = 1 x 476 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 476 is 1
Notice that 1 = HCF(476,1) .
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 723, 443, 476?
Answer: HCF of 723, 443, 476 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 723, 443, 476 using Euclid's Algorithm?
Answer: For arbitrary numbers 723, 443, 476 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.