Highest Common Factor of 212, 782 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 212, 782 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 212, 782 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 212, 782 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 212, 782 is 2.
HCF(212, 782) = 2
HCF of 212, 782 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 212, 782 is 2.
Highest Common Factor of 212,782 is 2
Step 1: Since 782 > 212, we apply the division lemma to 782 and 212, to get
782 = 212 x 3 + 146
Step 2: Since the reminder 212 ≠ 0, we apply division lemma to 146 and 212, to get
212 = 146 x 1 + 66
Step 3: We consider the new divisor 146 and the new remainder 66, and apply the division lemma to get
146 = 66 x 2 + 14
We consider the new divisor 66 and the new remainder 14,and apply the division lemma to get
66 = 14 x 4 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 212 and 782 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(66,14) = HCF(146,66) = HCF(212,146) = HCF(782,212) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 212, 782 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 212, 782?
Answer: HCF of 212, 782 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 212, 782 using Euclid's Algorithm?
Answer: For arbitrary numbers 212, 782 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.