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 168, 812, 610 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 168, 812, 610 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 168, 812, 610 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 168, 812, 610 is 2.
HCF(168, 812, 610) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 168, 812, 610 is 2.
Step 1: Since 812 > 168, we apply the division lemma to 812 and 168, to get
812 = 168 x 4 + 140
Step 2: Since the reminder 168 ≠ 0, we apply division lemma to 140 and 168, to get
168 = 140 x 1 + 28
Step 3: We consider the new divisor 140 and the new remainder 28, and apply the division lemma to get
140 = 28 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 28, the HCF of 168 and 812 is 28
Notice that 28 = HCF(140,28) = HCF(168,140) = HCF(812,168) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 610 > 28, we apply the division lemma to 610 and 28, to get
610 = 28 x 21 + 22
Step 2: Since the reminder 28 ≠ 0, we apply division lemma to 22 and 28, to get
28 = 22 x 1 + 6
Step 3: We consider the new divisor 22 and the new remainder 6, and apply the division lemma to get
22 = 6 x 3 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma 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 28 and 610 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(28,22) = HCF(610,28) .
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 168, 812, 610?
Answer: HCF of 168, 812, 610 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 168, 812, 610 using Euclid's Algorithm?
Answer: For arbitrary numbers 168, 812, 610 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.