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, 290, 777 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 493, 290, 777 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, 290, 777 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, 290, 777 is 1.
HCF(493, 290, 777) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 493, 290, 777 is 1.
Step 1: Since 493 > 290, we apply the division lemma to 493 and 290, to get
493 = 290 x 1 + 203
Step 2: Since the reminder 290 ≠ 0, we apply division lemma to 203 and 290, to get
290 = 203 x 1 + 87
Step 3: We consider the new divisor 203 and the new remainder 87, and apply the division lemma to get
203 = 87 x 2 + 29
We consider the new divisor 87 and the new remainder 29, and apply the division lemma to get
87 = 29 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 29, the HCF of 493 and 290 is 29
Notice that 29 = HCF(87,29) = HCF(203,87) = HCF(290,203) = HCF(493,290) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 777 > 29, we apply the division lemma to 777 and 29, to get
777 = 29 x 26 + 23
Step 2: Since the reminder 29 ≠ 0, we apply division lemma to 23 and 29, to get
29 = 23 x 1 + 6
Step 3: We consider the new divisor 23 and the new remainder 6, and apply the division lemma to get
23 = 6 x 3 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 29 and 777 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(23,6) = HCF(29,23) = HCF(777,29) .
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, 290, 777?
Answer: HCF of 493, 290, 777 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 493, 290, 777 using Euclid's Algorithm?
Answer: For arbitrary numbers 493, 290, 777 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.