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, 666, 867 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 257, 666, 867 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, 666, 867 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, 666, 867 is 1.
HCF(257, 666, 867) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 257, 666, 867 is 1.
Step 1: Since 666 > 257, we apply the division lemma to 666 and 257, to get
666 = 257 x 2 + 152
Step 2: Since the reminder 257 ≠ 0, we apply division lemma to 152 and 257, to get
257 = 152 x 1 + 105
Step 3: We consider the new divisor 152 and the new remainder 105, and apply the division lemma to get
152 = 105 x 1 + 47
We consider the new divisor 105 and the new remainder 47,and apply the division lemma to get
105 = 47 x 2 + 11
We consider the new divisor 47 and the new remainder 11,and apply the division lemma to get
47 = 11 x 4 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 257 and 666 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(47,11) = HCF(105,47) = HCF(152,105) = HCF(257,152) = HCF(666,257) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 867 > 1, we apply the division lemma to 867 and 1, to get
867 = 1 x 867 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 867 is 1
Notice that 1 = HCF(867,1) .
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, 666, 867?
Answer: HCF of 257, 666, 867 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 257, 666, 867 using Euclid's Algorithm?
Answer: For arbitrary numbers 257, 666, 867 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.