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, 6405, 1049 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 503, 6405, 1049 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, 6405, 1049 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, 6405, 1049 is 1.
HCF(503, 6405, 1049) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 503, 6405, 1049 is 1.
Step 1: Since 6405 > 503, we apply the division lemma to 6405 and 503, to get
6405 = 503 x 12 + 369
Step 2: Since the reminder 503 ≠ 0, we apply division lemma to 369 and 503, to get
503 = 369 x 1 + 134
Step 3: We consider the new divisor 369 and the new remainder 134, and apply the division lemma to get
369 = 134 x 2 + 101
We consider the new divisor 134 and the new remainder 101,and apply the division lemma to get
134 = 101 x 1 + 33
We consider the new divisor 101 and the new remainder 33,and apply the division lemma to get
101 = 33 x 3 + 2
We consider the new divisor 33 and the new remainder 2,and apply the division lemma to get
33 = 2 x 16 + 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 6405 is 1
Notice that 1 = HCF(2,1) = HCF(33,2) = HCF(101,33) = HCF(134,101) = HCF(369,134) = HCF(503,369) = HCF(6405,503) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1049 > 1, we apply the division lemma to 1049 and 1, to get
1049 = 1 x 1049 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 1049 is 1
Notice that 1 = HCF(1049,1) .
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, 6405, 1049?
Answer: HCF of 503, 6405, 1049 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 503, 6405, 1049 using Euclid's Algorithm?
Answer: For arbitrary numbers 503, 6405, 1049 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.