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 648, 2162 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 648, 2162 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 648, 2162 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 648, 2162 is 2.
HCF(648, 2162) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 648, 2162 is 2.
Step 1: Since 2162 > 648, we apply the division lemma to 2162 and 648, to get
2162 = 648 x 3 + 218
Step 2: Since the reminder 648 ≠ 0, we apply division lemma to 218 and 648, to get
648 = 218 x 2 + 212
Step 3: We consider the new divisor 218 and the new remainder 212, and apply the division lemma to get
218 = 212 x 1 + 6
We consider the new divisor 212 and the new remainder 6,and apply the division lemma to get
212 = 6 x 35 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 648 and 2162 is 2
Notice that 2 = HCF(6,2) = HCF(212,6) = HCF(218,212) = HCF(648,218) = HCF(2162,648) .
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 648, 2162?
Answer: HCF of 648, 2162 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 648, 2162 using Euclid's Algorithm?
Answer: For arbitrary numbers 648, 2162 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.