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 590, 216, 472 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 590, 216, 472 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 590, 216, 472 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 590, 216, 472 is 2.
HCF(590, 216, 472) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 590, 216, 472 is 2.
Step 1: Since 590 > 216, we apply the division lemma to 590 and 216, to get
590 = 216 x 2 + 158
Step 2: Since the reminder 216 ≠ 0, we apply division lemma to 158 and 216, to get
216 = 158 x 1 + 58
Step 3: We consider the new divisor 158 and the new remainder 58, and apply the division lemma to get
158 = 58 x 2 + 42
We consider the new divisor 58 and the new remainder 42,and apply the division lemma to get
58 = 42 x 1 + 16
We consider the new divisor 42 and the new remainder 16,and apply the division lemma to get
42 = 16 x 2 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 590 and 216 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(42,16) = HCF(58,42) = HCF(158,58) = HCF(216,158) = HCF(590,216) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 472 > 2, we apply the division lemma to 472 and 2, to get
472 = 2 x 236 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 472 is 2
Notice that 2 = HCF(472,2) .
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 590, 216, 472?
Answer: HCF of 590, 216, 472 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 590, 216, 472 using Euclid's Algorithm?
Answer: For arbitrary numbers 590, 216, 472 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.