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, 811, 660 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 503, 811, 660 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, 811, 660 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, 811, 660 is 1.
HCF(503, 811, 660) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 503, 811, 660 is 1.
Step 1: Since 811 > 503, we apply the division lemma to 811 and 503, to get
811 = 503 x 1 + 308
Step 2: Since the reminder 503 ≠ 0, we apply division lemma to 308 and 503, to get
503 = 308 x 1 + 195
Step 3: We consider the new divisor 308 and the new remainder 195, and apply the division lemma to get
308 = 195 x 1 + 113
We consider the new divisor 195 and the new remainder 113,and apply the division lemma to get
195 = 113 x 1 + 82
We consider the new divisor 113 and the new remainder 82,and apply the division lemma to get
113 = 82 x 1 + 31
We consider the new divisor 82 and the new remainder 31,and apply the division lemma to get
82 = 31 x 2 + 20
We consider the new divisor 31 and the new remainder 20,and apply the division lemma to get
31 = 20 x 1 + 11
We consider the new divisor 20 and the new remainder 11,and apply the division lemma to get
20 = 11 x 1 + 9
We consider the new divisor 11 and the new remainder 9,and apply the division lemma to get
11 = 9 x 1 + 2
We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get
9 = 2 x 4 + 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 811 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(20,11) = HCF(31,20) = HCF(82,31) = HCF(113,82) = HCF(195,113) = HCF(308,195) = HCF(503,308) = HCF(811,503) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 660 > 1, we apply the division lemma to 660 and 1, to get
660 = 1 x 660 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 660 is 1
Notice that 1 = HCF(660,1) .
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 503, 811, 660?
Answer: HCF of 503, 811, 660 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 503, 811, 660 using Euclid's Algorithm?
Answer: For arbitrary numbers 503, 811, 660 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.