Highest Common Factor of 503, 322, 498 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 503, 322, 498 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 503, 322, 498 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 503, 322, 498 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 503, 322, 498 is 1.
HCF(503, 322, 498) = 1
HCF of 503, 322, 498 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 503, 322, 498 is 1.
Highest Common Factor of 503,322,498 is 1
Step 1: Since 503 > 322, we apply the division lemma to 503 and 322, to get
503 = 322 x 1 + 181
Step 2: Since the reminder 322 ≠ 0, we apply division lemma to 181 and 322, to get
322 = 181 x 1 + 141
Step 3: We consider the new divisor 181 and the new remainder 141, and apply the division lemma to get
181 = 141 x 1 + 40
We consider the new divisor 141 and the new remainder 40,and apply the division lemma to get
141 = 40 x 3 + 21
We consider the new divisor 40 and the new remainder 21,and apply the division lemma to get
40 = 21 x 1 + 19
We consider the new divisor 21 and the new remainder 19,and apply the division lemma to get
21 = 19 x 1 + 2
We consider the new divisor 19 and the new remainder 2,and apply the division lemma to get
19 = 2 x 9 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 503 and 322 is 1
Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(21,19) = HCF(40,21) = HCF(141,40) = HCF(181,141) = HCF(322,181) = HCF(503,322) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 498 > 1, we apply the division lemma to 498 and 1, to get
498 = 1 x 498 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 498 is 1
Notice that 1 = HCF(498,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 503, 322, 498 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 503, 322, 498?
Answer: HCF of 503, 322, 498 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 503, 322, 498 using Euclid's Algorithm?
Answer: For arbitrary numbers 503, 322, 498 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.