Highest Common Factor of 97, 345 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 97, 345 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 97, 345 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 97, 345 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 97, 345 is 1.
HCF(97, 345) = 1
HCF of 97, 345 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 97, 345 is 1.
Highest Common Factor of 97,345 is 1
Step 1: Since 345 > 97, we apply the division lemma to 345 and 97, to get
345 = 97 x 3 + 54
Step 2: Since the reminder 97 ≠ 0, we apply division lemma to 54 and 97, to get
97 = 54 x 1 + 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 97 and 345 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(43,11) = HCF(54,43) = HCF(97,54) = HCF(345,97) .
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Frequently Asked Questions on HCF of 97, 345 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 97, 345?
Answer: HCF of 97, 345 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 97, 345 using Euclid's Algorithm?
Answer: For arbitrary numbers 97, 345 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.