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, 456, 749 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 723, 456, 749 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, 456, 749 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, 456, 749 is 1.
HCF(723, 456, 749) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 723, 456, 749 is 1.
Step 1: Since 723 > 456, we apply the division lemma to 723 and 456, to get
723 = 456 x 1 + 267
Step 2: Since the reminder 456 ≠ 0, we apply division lemma to 267 and 456, to get
456 = 267 x 1 + 189
Step 3: We consider the new divisor 267 and the new remainder 189, and apply the division lemma to get
267 = 189 x 1 + 78
We consider the new divisor 189 and the new remainder 78,and apply the division lemma to get
189 = 78 x 2 + 33
We consider the new divisor 78 and the new remainder 33,and apply the division lemma to get
78 = 33 x 2 + 12
We consider the new divisor 33 and the new remainder 12,and apply the division lemma to get
33 = 12 x 2 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 723 and 456 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(33,12) = HCF(78,33) = HCF(189,78) = HCF(267,189) = HCF(456,267) = HCF(723,456) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 749 > 3, we apply the division lemma to 749 and 3, to get
749 = 3 x 249 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 749 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(749,3) .
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, 456, 749?
Answer: HCF of 723, 456, 749 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 723, 456, 749 using Euclid's Algorithm?
Answer: For arbitrary numbers 723, 456, 749 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.