Highest Common Factor of 113, 198, 233 using Euclid's algorithm
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 113, 198, 233 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 113, 198, 233 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 113, 198, 233 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 113, 198, 233 is 1.
HCF(113, 198, 233) = 1
HCF of 113, 198, 233 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 113, 198, 233 is 1.
Highest Common Factor of 113,198,233 is 1
Step 1: Since 198 > 113, we apply the division lemma to 198 and 113, to get
198 = 113 x 1 + 85
Step 2: Since the reminder 113 ≠ 0, we apply division lemma to 85 and 113, to get
113 = 85 x 1 + 28
Step 3: We consider the new divisor 85 and the new remainder 28, and apply the division lemma to get
85 = 28 x 3 + 1
We consider the new divisor 28 and the new remainder 1, and apply the division lemma to get
28 = 1 x 28 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 113 and 198 is 1
Notice that 1 = HCF(28,1) = HCF(85,28) = HCF(113,85) = HCF(198,113) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 233 > 1, we apply the division lemma to 233 and 1, to get
233 = 1 x 233 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 233 is 1
Notice that 1 = HCF(233,1) .
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Frequently Asked Questions on HCF of 113, 198, 233 using Euclid's Algorithm
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 113, 198, 233?
Answer: HCF of 113, 198, 233 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 113, 198, 233 using Euclid's Algorithm?
Answer: For arbitrary numbers 113, 198, 233 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.