Highest Common Factor of 23, 80, 31, 238 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 23, 80, 31, 238 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 23, 80, 31, 238 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 23, 80, 31, 238 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 23, 80, 31, 238 is 1.
HCF(23, 80, 31, 238) = 1
HCF of 23, 80, 31, 238 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 23, 80, 31, 238 is 1.
Highest Common Factor of 23,80,31,238 is 1
Step 1: Since 80 > 23, we apply the division lemma to 80 and 23, to get
80 = 23 x 3 + 11
Step 2: Since the reminder 23 ≠ 0, we apply division lemma to 11 and 23, to get
23 = 11 x 2 + 1
Step 3: We consider the new divisor 11 and the new remainder 1, and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 23 and 80 is 1
Notice that 1 = HCF(11,1) = HCF(23,11) = HCF(80,23) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 31 > 1, we apply the division lemma to 31 and 1, to get
31 = 1 x 31 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 31 is 1
Notice that 1 = HCF(31,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 238 > 1, we apply the division lemma to 238 and 1, to get
238 = 1 x 238 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 238 is 1
Notice that 1 = HCF(238,1) .
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Frequently Asked Questions on HCF of 23, 80, 31, 238 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 23, 80, 31, 238?
Answer: HCF of 23, 80, 31, 238 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 23, 80, 31, 238 using Euclid's Algorithm?
Answer: For arbitrary numbers 23, 80, 31, 238 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.