Highest Common Factor of 343, 9785 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 343, 9785 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 343, 9785 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 343, 9785 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 343, 9785 is 1.
HCF(343, 9785) = 1
HCF of 343, 9785 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 343, 9785 is 1.
Highest Common Factor of 343,9785 is 1
Step 1: Since 9785 > 343, we apply the division lemma to 9785 and 343, to get
9785 = 343 x 28 + 181
Step 2: Since the reminder 343 ≠ 0, we apply division lemma to 181 and 343, to get
343 = 181 x 1 + 162
Step 3: We consider the new divisor 181 and the new remainder 162, and apply the division lemma to get
181 = 162 x 1 + 19
We consider the new divisor 162 and the new remainder 19,and apply the division lemma to get
162 = 19 x 8 + 10
We consider the new divisor 19 and the new remainder 10,and apply the division lemma to get
19 = 10 x 1 + 9
We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get
10 = 9 x 1 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 343 and 9785 is 1
Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(19,10) = HCF(162,19) = HCF(181,162) = HCF(343,181) = HCF(9785,343) .
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Frequently Asked Questions on HCF of 343, 9785 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 343, 9785?
Answer: HCF of 343, 9785 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 343, 9785 using Euclid's Algorithm?
Answer: For arbitrary numbers 343, 9785 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.