Highest Common Factor of 151, 205 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 151, 205 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 151, 205 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 151, 205 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 151, 205 is 1.
HCF(151, 205) = 1
HCF of 151, 205 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 151, 205 is 1.
Highest Common Factor of 151,205 is 1
Step 1: Since 205 > 151, we apply the division lemma to 205 and 151, to get
205 = 151 x 1 + 54
Step 2: Since the reminder 151 ≠ 0, we apply division lemma to 54 and 151, to get
151 = 54 x 2 + 43
Step 3: We consider the new divisor 54 and the new remainder 43, and apply the division lemma to get
54 = 43 x 1 + 11
We consider the new divisor 43 and the new remainder 11,and apply the division lemma to get
43 = 11 x 3 + 10
We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get
11 = 10 x 1 + 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 151 and 205 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(43,11) = HCF(54,43) = HCF(151,54) = HCF(205,151) .
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Frequently Asked Questions on HCF of 151, 205 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 151, 205?
Answer: HCF of 151, 205 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 151, 205 using Euclid's Algorithm?
Answer: For arbitrary numbers 151, 205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.