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 493, 348, 28 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 493, 348, 28 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 493, 348, 28 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 493, 348, 28 is 1.
HCF(493, 348, 28) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 493, 348, 28 is 1.
Step 1: Since 493 > 348, we apply the division lemma to 493 and 348, to get
493 = 348 x 1 + 145
Step 2: Since the reminder 348 ≠ 0, we apply division lemma to 145 and 348, to get
348 = 145 x 2 + 58
Step 3: We consider the new divisor 145 and the new remainder 58, and apply the division lemma to get
145 = 58 x 2 + 29
We consider the new divisor 58 and the new remainder 29, and apply the division lemma to get
58 = 29 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 29, the HCF of 493 and 348 is 29
Notice that 29 = HCF(58,29) = HCF(145,58) = HCF(348,145) = HCF(493,348) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 29 > 28, we apply the division lemma to 29 and 28, to get
29 = 28 x 1 + 1
Step 2: Since the reminder 28 ≠ 0, we apply division lemma to 1 and 28, to get
28 = 1 x 28 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 29 and 28 is 1
Notice that 1 = HCF(28,1) = HCF(29,28) .
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 493, 348, 28?
Answer: HCF of 493, 348, 28 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 493, 348, 28 using Euclid's Algorithm?
Answer: For arbitrary numbers 493, 348, 28 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.