Highest Common Factor of 570, 3204 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 570, 3204 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 570, 3204 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 570, 3204 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 570, 3204 is 6.
HCF(570, 3204) = 6
HCF of 570, 3204 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 570, 3204 is 6.
Highest Common Factor of 570,3204 is 6
Step 1: Since 3204 > 570, we apply the division lemma to 3204 and 570, to get
3204 = 570 x 5 + 354
Step 2: Since the reminder 570 ≠ 0, we apply division lemma to 354 and 570, to get
570 = 354 x 1 + 216
Step 3: We consider the new divisor 354 and the new remainder 216, and apply the division lemma to get
354 = 216 x 1 + 138
We consider the new divisor 216 and the new remainder 138,and apply the division lemma to get
216 = 138 x 1 + 78
We consider the new divisor 138 and the new remainder 78,and apply the division lemma to get
138 = 78 x 1 + 60
We consider the new divisor 78 and the new remainder 60,and apply the division lemma to get
78 = 60 x 1 + 18
We consider the new divisor 60 and the new remainder 18,and apply the division lemma to get
60 = 18 x 3 + 6
We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 570 and 3204 is 6
Notice that 6 = HCF(18,6) = HCF(60,18) = HCF(78,60) = HCF(138,78) = HCF(216,138) = HCF(354,216) = HCF(570,354) = HCF(3204,570) .
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Frequently Asked Questions on HCF of 570, 3204 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 570, 3204?
Answer: HCF of 570, 3204 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 570, 3204 using Euclid's Algorithm?
Answer: For arbitrary numbers 570, 3204 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.