Highest Common Factor of 374, 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 374, 205 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 374, 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 374, 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 374, 205 is 1.
HCF(374, 205) = 1
HCF of 374, 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 374, 205 is 1.
Highest Common Factor of 374,205 is 1
Step 1: Since 374 > 205, we apply the division lemma to 374 and 205, to get
374 = 205 x 1 + 169
Step 2: Since the reminder 205 ≠ 0, we apply division lemma to 169 and 205, to get
205 = 169 x 1 + 36
Step 3: We consider the new divisor 169 and the new remainder 36, and apply the division lemma to get
169 = 36 x 4 + 25
We consider the new divisor 36 and the new remainder 25,and apply the division lemma to get
36 = 25 x 1 + 11
We consider the new divisor 25 and the new remainder 11,and apply the division lemma to get
25 = 11 x 2 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 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 374 and 205 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(25,11) = HCF(36,25) = HCF(169,36) = HCF(205,169) = HCF(374,205) .
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Frequently Asked Questions on HCF of 374, 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 374, 205?
Answer: HCF of 374, 205 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 374, 205 using Euclid's Algorithm?
Answer: For arbitrary numbers 374, 205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.