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 257, 731, 204, 268 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 257, 731, 204, 268 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 257, 731, 204, 268 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 257, 731, 204, 268 is 1.
HCF(257, 731, 204, 268) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 257, 731, 204, 268 is 1.
Step 1: Since 731 > 257, we apply the division lemma to 731 and 257, to get
731 = 257 x 2 + 217
Step 2: Since the reminder 257 ≠ 0, we apply division lemma to 217 and 257, to get
257 = 217 x 1 + 40
Step 3: We consider the new divisor 217 and the new remainder 40, and apply the division lemma to get
217 = 40 x 5 + 17
We consider the new divisor 40 and the new remainder 17,and apply the division lemma to get
40 = 17 x 2 + 6
We consider the new divisor 17 and the new remainder 6,and apply the division lemma to get
17 = 6 x 2 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 257 and 731 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(17,6) = HCF(40,17) = HCF(217,40) = HCF(257,217) = HCF(731,257) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 204 > 1, we apply the division lemma to 204 and 1, to get
204 = 1 x 204 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 204 is 1
Notice that 1 = HCF(204,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 268 > 1, we apply the division lemma to 268 and 1, to get
268 = 1 x 268 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 268 is 1
Notice that 1 = HCF(268,1) .
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 257, 731, 204, 268?
Answer: HCF of 257, 731, 204, 268 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 257, 731, 204, 268 using Euclid's Algorithm?
Answer: For arbitrary numbers 257, 731, 204, 268 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.