Highest Common Factor of 588, 9738 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, 9738 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 588, 9738 is 6 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, 9738 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, 9738 is 6.
HCF(588, 9738) = 6
HCF of 588, 9738 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, 9738 is 6.
Highest Common Factor of 588,9738 is 6
Step 1: Since 9738 > 588, we apply the division lemma to 9738 and 588, to get
9738 = 588 x 16 + 330
Step 2: Since the reminder 588 ≠ 0, we apply division lemma to 330 and 588, to get
588 = 330 x 1 + 258
Step 3: We consider the new divisor 330 and the new remainder 258, and apply the division lemma to get
330 = 258 x 1 + 72
We consider the new divisor 258 and the new remainder 72,and apply the division lemma to get
258 = 72 x 3 + 42
We consider the new divisor 72 and the new remainder 42,and apply the division lemma to get
72 = 42 x 1 + 30
We consider the new divisor 42 and the new remainder 30,and apply the division lemma to get
42 = 30 x 1 + 12
We consider the new divisor 30 and the new remainder 12,and apply the division lemma to get
30 = 12 x 2 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 588 and 9738 is 6
Notice that 6 = HCF(12,6) = HCF(30,12) = HCF(42,30) = HCF(72,42) = HCF(258,72) = HCF(330,258) = HCF(588,330) = HCF(9738,588) .
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Frequently Asked Questions on HCF of 588, 9738 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, 9738?
Answer: HCF of 588, 9738 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 588, 9738 using Euclid's Algorithm?
Answer: For arbitrary numbers 588, 9738 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.