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, 5708, 3010 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 216, 5708, 3010 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, 5708, 3010 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, 5708, 3010 is 2.
HCF(216, 5708, 3010) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 216, 5708, 3010 is 2.
Step 1: Since 5708 > 216, we apply the division lemma to 5708 and 216, to get
5708 = 216 x 26 + 92
Step 2: Since the reminder 216 ≠ 0, we apply division lemma to 92 and 216, to get
216 = 92 x 2 + 32
Step 3: We consider the new divisor 92 and the new remainder 32, and apply the division lemma to get
92 = 32 x 2 + 28
We consider the new divisor 32 and the new remainder 28,and apply the division lemma to get
32 = 28 x 1 + 4
We consider the new divisor 28 and the new remainder 4,and apply the division lemma to get
28 = 4 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 216 and 5708 is 4
Notice that 4 = HCF(28,4) = HCF(32,28) = HCF(92,32) = HCF(216,92) = HCF(5708,216) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3010 > 4, we apply the division lemma to 3010 and 4, to get
3010 = 4 x 752 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 3010 is 2
Notice that 2 = HCF(4,2) = HCF(3010,4) .
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, 5708, 3010?
Answer: HCF of 216, 5708, 3010 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 216, 5708, 3010 using Euclid's Algorithm?
Answer: For arbitrary numbers 216, 5708, 3010 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.