Highest Common Factor of 145, 343 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 145, 343 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 145, 343 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 145, 343 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 145, 343 is 1.
HCF(145, 343) = 1
HCF of 145, 343 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 145, 343 is 1.
Highest Common Factor of 145,343 is 1
Step 1: Since 343 > 145, we apply the division lemma to 343 and 145, to get
343 = 145 x 2 + 53
Step 2: Since the reminder 145 ≠ 0, we apply division lemma to 53 and 145, to get
145 = 53 x 2 + 39
Step 3: We consider the new divisor 53 and the new remainder 39, and apply the division lemma to get
53 = 39 x 1 + 14
We consider the new divisor 39 and the new remainder 14,and apply the division lemma to get
39 = 14 x 2 + 11
We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get
14 = 11 x 1 + 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 145 and 343 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(39,14) = HCF(53,39) = HCF(145,53) = HCF(343,145) .
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Frequently Asked Questions on HCF of 145, 343 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 145, 343?
Answer: HCF of 145, 343 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 145, 343 using Euclid's Algorithm?
Answer: For arbitrary numbers 145, 343 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.