Highest Common Factor of 420, 816, 570 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 420, 816, 570 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 420, 816, 570 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 420, 816, 570 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 420, 816, 570 is 6.
HCF(420, 816, 570) = 6
HCF of 420, 816, 570 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 420, 816, 570 is 6.
Highest Common Factor of 420,816,570 is 6
Step 1: Since 816 > 420, we apply the division lemma to 816 and 420, to get
816 = 420 x 1 + 396
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 396 and 420, to get
420 = 396 x 1 + 24
Step 3: We consider the new divisor 396 and the new remainder 24, and apply the division lemma to get
396 = 24 x 16 + 12
We consider the new divisor 24 and the new remainder 12, and apply the division lemma to get
24 = 12 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 420 and 816 is 12
Notice that 12 = HCF(24,12) = HCF(396,24) = HCF(420,396) = HCF(816,420) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 570 > 12, we apply the division lemma to 570 and 12, to get
570 = 12 x 47 + 6
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 6 and 12, 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 12 and 570 is 6
Notice that 6 = HCF(12,6) = HCF(570,12) .
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Frequently Asked Questions on HCF of 420, 816, 570 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 420, 816, 570?
Answer: HCF of 420, 816, 570 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 420, 816, 570 using Euclid's Algorithm?
Answer: For arbitrary numbers 420, 816, 570 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.