Highest Common Factor of 612, 832 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 612, 832 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 612, 832 is 4 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 612, 832 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 612, 832 is 4.
HCF(612, 832) = 4
HCF of 612, 832 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 612, 832 is 4.
Highest Common Factor of 612,832 is 4
Step 1: Since 832 > 612, we apply the division lemma to 832 and 612, to get
832 = 612 x 1 + 220
Step 2: Since the reminder 612 ≠ 0, we apply division lemma to 220 and 612, to get
612 = 220 x 2 + 172
Step 3: We consider the new divisor 220 and the new remainder 172, and apply the division lemma to get
220 = 172 x 1 + 48
We consider the new divisor 172 and the new remainder 48,and apply the division lemma to get
172 = 48 x 3 + 28
We consider the new divisor 48 and the new remainder 28,and apply the division lemma to get
48 = 28 x 1 + 20
We consider the new divisor 28 and the new remainder 20,and apply the division lemma to get
28 = 20 x 1 + 8
We consider the new divisor 20 and the new remainder 8,and apply the division lemma to get
20 = 8 x 2 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 612 and 832 is 4
Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(28,20) = HCF(48,28) = HCF(172,48) = HCF(220,172) = HCF(612,220) = HCF(832,612) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 612, 832 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 612, 832?
Answer: HCF of 612, 832 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 612, 832 using Euclid's Algorithm?
Answer: For arbitrary numbers 612, 832 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.