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 273, 462, 472 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 273, 462, 472 is 1 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 273, 462, 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 273, 462, 472 is 1.
HCF(273, 462, 472) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 273, 462, 472 is 1.
Step 1: Since 462 > 273, we apply the division lemma to 462 and 273, to get
462 = 273 x 1 + 189
Step 2: Since the reminder 273 ≠ 0, we apply division lemma to 189 and 273, to get
273 = 189 x 1 + 84
Step 3: We consider the new divisor 189 and the new remainder 84, and apply the division lemma to get
189 = 84 x 2 + 21
We consider the new divisor 84 and the new remainder 21, and apply the division lemma to get
84 = 21 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 273 and 462 is 21
Notice that 21 = HCF(84,21) = HCF(189,84) = HCF(273,189) = HCF(462,273) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 472 > 21, we apply the division lemma to 472 and 21, to get
472 = 21 x 22 + 10
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 10 and 21, to get
21 = 10 x 2 + 1
Step 3: We consider the new divisor 10 and the new remainder 1, and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 21 and 472 is 1
Notice that 1 = HCF(10,1) = HCF(21,10) = HCF(472,21) .
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 273, 462, 472?
Answer: HCF of 273, 462, 472 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 273, 462, 472 using Euclid's Algorithm?
Answer: For arbitrary numbers 273, 462, 472 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.