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 505, 194, 493 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 505, 194, 493 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 505, 194, 493 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 505, 194, 493 is 1.
HCF(505, 194, 493) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 505, 194, 493 is 1.
Step 1: Since 505 > 194, we apply the division lemma to 505 and 194, to get
505 = 194 x 2 + 117
Step 2: Since the reminder 194 ≠ 0, we apply division lemma to 117 and 194, to get
194 = 117 x 1 + 77
Step 3: We consider the new divisor 117 and the new remainder 77, and apply the division lemma to get
117 = 77 x 1 + 40
We consider the new divisor 77 and the new remainder 40,and apply the division lemma to get
77 = 40 x 1 + 37
We consider the new divisor 40 and the new remainder 37,and apply the division lemma to get
40 = 37 x 1 + 3
We consider the new divisor 37 and the new remainder 3,and apply the division lemma to get
37 = 3 x 12 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 505 and 194 is 1
Notice that 1 = HCF(3,1) = HCF(37,3) = HCF(40,37) = HCF(77,40) = HCF(117,77) = HCF(194,117) = HCF(505,194) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 493 > 1, we apply the division lemma to 493 and 1, to get
493 = 1 x 493 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 493 is 1
Notice that 1 = HCF(493,1) .
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 505, 194, 493?
Answer: HCF of 505, 194, 493 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 505, 194, 493 using Euclid's Algorithm?
Answer: For arbitrary numbers 505, 194, 493 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.