Highest Common Factor of 738, 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 738, 343 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 738, 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 738, 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 738, 343 is 1.
HCF(738, 343) = 1
HCF of 738, 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 738, 343 is 1.
Highest Common Factor of 738,343 is 1
Step 1: Since 738 > 343, we apply the division lemma to 738 and 343, to get
738 = 343 x 2 + 52
Step 2: Since the reminder 343 ≠ 0, we apply division lemma to 52 and 343, to get
343 = 52 x 6 + 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 738 and 343 is 1
Notice that 1 = HCF(10,1) = HCF(21,10) = HCF(31,21) = HCF(52,31) = HCF(343,52) = HCF(738,343) .
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Frequently Asked Questions on HCF of 738, 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 738, 343?
Answer: HCF of 738, 343 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 738, 343 using Euclid's Algorithm?
Answer: For arbitrary numbers 738, 343 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.