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 216, 946 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 216, 946 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 216, 946 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 216, 946 is 2.
HCF(216, 946) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 216, 946 is 2.
Step 1: Since 946 > 216, we apply the division lemma to 946 and 216, to get
946 = 216 x 4 + 82
Step 2: Since the reminder 216 ≠ 0, we apply division lemma to 82 and 216, to get
216 = 82 x 2 + 52
Step 3: We consider the new divisor 82 and the new remainder 52, and apply the division lemma to get
82 = 52 x 1 + 30
We consider the new divisor 52 and the new remainder 30,and apply the division lemma to get
52 = 30 x 1 + 22
We consider the new divisor 30 and the new remainder 22,and apply the division lemma to get
30 = 22 x 1 + 8
We consider the new divisor 22 and the new remainder 8,and apply the division lemma to get
22 = 8 x 2 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 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 216 and 946 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(22,8) = HCF(30,22) = HCF(52,30) = HCF(82,52) = HCF(216,82) = HCF(946,216) .
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 216, 946?
Answer: HCF of 216, 946 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 216, 946 using Euclid's Algorithm?
Answer: For arbitrary numbers 216, 946 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.