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 233, 635, 398 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 233, 635, 398 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 233, 635, 398 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 233, 635, 398 is 1.
HCF(233, 635, 398) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 233, 635, 398 is 1.
Step 1: Since 635 > 233, we apply the division lemma to 635 and 233, to get
635 = 233 x 2 + 169
Step 2: Since the reminder 233 ≠ 0, we apply division lemma to 169 and 233, to get
233 = 169 x 1 + 64
Step 3: We consider the new divisor 169 and the new remainder 64, and apply the division lemma to get
169 = 64 x 2 + 41
We consider the new divisor 64 and the new remainder 41,and apply the division lemma to get
64 = 41 x 1 + 23
We consider the new divisor 41 and the new remainder 23,and apply the division lemma to get
41 = 23 x 1 + 18
We consider the new divisor 23 and the new remainder 18,and apply the division lemma to get
23 = 18 x 1 + 5
We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get
18 = 5 x 3 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 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 233 and 635 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(23,18) = HCF(41,23) = HCF(64,41) = HCF(169,64) = HCF(233,169) = HCF(635,233) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 398 > 1, we apply the division lemma to 398 and 1, to get
398 = 1 x 398 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 398 is 1
Notice that 1 = HCF(398,1) .
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 233, 635, 398?
Answer: HCF of 233, 635, 398 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 233, 635, 398 using Euclid's Algorithm?
Answer: For arbitrary numbers 233, 635, 398 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.