Highest Common Factor of 588, 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 588, 345 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 588, 345 is 3 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 588, 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 588, 345 is 3.
HCF(588, 345) = 3
HCF of 588, 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 588, 345 is 3.
Highest Common Factor of 588,345 is 3
Step 1: Since 588 > 345, we apply the division lemma to 588 and 345, to get
588 = 345 x 1 + 243
Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 243 and 345, to get
345 = 243 x 1 + 102
Step 3: We consider the new divisor 243 and the new remainder 102, and apply the division lemma to get
243 = 102 x 2 + 39
We consider the new divisor 102 and the new remainder 39,and apply the division lemma to get
102 = 39 x 2 + 24
We consider the new divisor 39 and the new remainder 24,and apply the division lemma to get
39 = 24 x 1 + 15
We consider the new divisor 24 and the new remainder 15,and apply the division lemma to get
24 = 15 x 1 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 588 and 345 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(24,15) = HCF(39,24) = HCF(102,39) = HCF(243,102) = HCF(345,243) = HCF(588,345) .
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Frequently Asked Questions on HCF of 588, 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 588, 345?
Answer: HCF of 588, 345 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 588, 345 using Euclid's Algorithm?
Answer: For arbitrary numbers 588, 345 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
