Highest Common Factor of 840, 471, 20 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 840, 471, 20 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 840, 471, 20 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 840, 471, 20 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 840, 471, 20 is 1.
HCF(840, 471, 20) = 1
HCF of 840, 471, 20 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 840, 471, 20 is 1.
Highest Common Factor of 840,471,20 is 1
Step 1: Since 840 > 471, we apply the division lemma to 840 and 471, to get
840 = 471 x 1 + 369
Step 2: Since the reminder 471 ≠ 0, we apply division lemma to 369 and 471, to get
471 = 369 x 1 + 102
Step 3: We consider the new divisor 369 and the new remainder 102, and apply the division lemma to get
369 = 102 x 3 + 63
We consider the new divisor 102 and the new remainder 63,and apply the division lemma to get
102 = 63 x 1 + 39
We consider the new divisor 63 and the new remainder 39,and apply the division lemma to get
63 = 39 x 1 + 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 840 and 471 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(24,15) = HCF(39,24) = HCF(63,39) = HCF(102,63) = HCF(369,102) = HCF(471,369) = HCF(840,471) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 20 > 3, we apply the division lemma to 20 and 3, to get
20 = 3 x 6 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 20 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(20,3) .
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Frequently Asked Questions on HCF of 840, 471, 20 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 840, 471, 20?
Answer: HCF of 840, 471, 20 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 840, 471, 20 using Euclid's Algorithm?
Answer: For arbitrary numbers 840, 471, 20 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
