Highest Common Factor of 83, 135, 257 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 83, 135, 257 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 83, 135, 257 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 83, 135, 257 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 83, 135, 257 is 1.
HCF(83, 135, 257) = 1
HCF of 83, 135, 257 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 83, 135, 257 is 1.
Highest Common Factor of 83,135,257 is 1
Step 1: Since 135 > 83, we apply the division lemma to 135 and 83, to get
135 = 83 x 1 + 52
Step 2: Since the reminder 83 ≠ 0, we apply division lemma to 52 and 83, to get
83 = 52 x 1 + 31
Step 3: We consider the new divisor 52 and the new remainder 31, and apply the division lemma to get
52 = 31 x 1 + 21
We consider the new divisor 31 and the new remainder 21,and apply the division lemma to get
31 = 21 x 1 + 10
We consider the new divisor 21 and the new remainder 10,and apply the division lemma to get
21 = 10 x 2 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 83 and 135 is 1
Notice that 1 = HCF(10,1) = HCF(21,10) = HCF(31,21) = HCF(52,31) = HCF(83,52) = HCF(135,83) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 257 > 1, we apply the division lemma to 257 and 1, to get
257 = 1 x 257 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 257 is 1
Notice that 1 = HCF(257,1) .
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Frequently Asked Questions on HCF of 83, 135, 257 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 83, 135, 257?
Answer: HCF of 83, 135, 257 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 83, 135, 257 using Euclid's Algorithm?
Answer: For arbitrary numbers 83, 135, 257 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
