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 724, 428, 830 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 724, 428, 830 is 2 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 724, 428, 830 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 724, 428, 830 is 2.
HCF(724, 428, 830) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 724, 428, 830 is 2.
Step 1: Since 724 > 428, we apply the division lemma to 724 and 428, to get
724 = 428 x 1 + 296
Step 2: Since the reminder 428 ≠ 0, we apply division lemma to 296 and 428, to get
428 = 296 x 1 + 132
Step 3: We consider the new divisor 296 and the new remainder 132, and apply the division lemma to get
296 = 132 x 2 + 32
We consider the new divisor 132 and the new remainder 32,and apply the division lemma to get
132 = 32 x 4 + 4
We consider the new divisor 32 and the new remainder 4,and apply the division lemma to get
32 = 4 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 724 and 428 is 4
Notice that 4 = HCF(32,4) = HCF(132,32) = HCF(296,132) = HCF(428,296) = HCF(724,428) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 830 > 4, we apply the division lemma to 830 and 4, to get
830 = 4 x 207 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 830 is 2
Notice that 2 = HCF(4,2) = HCF(830,4) .
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 724, 428, 830?
Answer: HCF of 724, 428, 830 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 724, 428, 830 using Euclid's Algorithm?
Answer: For arbitrary numbers 724, 428, 830 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.