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 812, 106 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 812, 106 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 812, 106 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 812, 106 is 2.
HCF(812, 106) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 812, 106 is 2.
Step 1: Since 812 > 106, we apply the division lemma to 812 and 106, to get
812 = 106 x 7 + 70
Step 2: Since the reminder 106 ≠ 0, we apply division lemma to 70 and 106, to get
106 = 70 x 1 + 36
Step 3: We consider the new divisor 70 and the new remainder 36, and apply the division lemma to get
70 = 36 x 1 + 34
We consider the new divisor 36 and the new remainder 34,and apply the division lemma to get
36 = 34 x 1 + 2
We consider the new divisor 34 and the new remainder 2,and apply the division lemma to get
34 = 2 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 812 and 106 is 2
Notice that 2 = HCF(34,2) = HCF(36,34) = HCF(70,36) = HCF(106,70) = HCF(812,106) .
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 812, 106?
Answer: HCF of 812, 106 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 812, 106 using Euclid's Algorithm?
Answer: For arbitrary numbers 812, 106 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.