Highest Common Factor of 497, 105, 511 using Euclid's algorithm
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 497, 105, 511 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 497, 105, 511 is 7 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 497, 105, 511 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 497, 105, 511 is 7.
HCF(497, 105, 511) = 7
HCF of 497, 105, 511 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 497, 105, 511 is 7.
Highest Common Factor of 497,105,511 is 7
Step 1: Since 497 > 105, we apply the division lemma to 497 and 105, to get
497 = 105 x 4 + 77
Step 2: Since the reminder 105 ≠ 0, we apply division lemma to 77 and 105, to get
105 = 77 x 1 + 28
Step 3: We consider the new divisor 77 and the new remainder 28, and apply the division lemma to get
77 = 28 x 2 + 21
We consider the new divisor 28 and the new remainder 21,and apply the division lemma to get
28 = 21 x 1 + 7
We consider the new divisor 21 and the new remainder 7,and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 497 and 105 is 7
Notice that 7 = HCF(21,7) = HCF(28,21) = HCF(77,28) = HCF(105,77) = HCF(497,105) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 511 > 7, we apply the division lemma to 511 and 7, to get
511 = 7 x 73 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 7 and 511 is 7
Notice that 7 = HCF(511,7) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 497, 105, 511 using Euclid's Algorithm
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 497, 105, 511?
Answer: HCF of 497, 105, 511 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 497, 105, 511 using Euclid's Algorithm?
Answer: For arbitrary numbers 497, 105, 511 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.