Highest Common Factor of 516, 846, 469 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 516, 846, 469 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 516, 846, 469 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 516, 846, 469 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 516, 846, 469 is 1.
HCF(516, 846, 469) = 1
HCF of 516, 846, 469 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 516, 846, 469 is 1.
Highest Common Factor of 516,846,469 is 1
Step 1: Since 846 > 516, we apply the division lemma to 846 and 516, to get
846 = 516 x 1 + 330
Step 2: Since the reminder 516 ≠ 0, we apply division lemma to 330 and 516, to get
516 = 330 x 1 + 186
Step 3: We consider the new divisor 330 and the new remainder 186, and apply the division lemma to get
330 = 186 x 1 + 144
We consider the new divisor 186 and the new remainder 144,and apply the division lemma to get
186 = 144 x 1 + 42
We consider the new divisor 144 and the new remainder 42,and apply the division lemma to get
144 = 42 x 3 + 18
We consider the new divisor 42 and the new remainder 18,and apply the division lemma to get
42 = 18 x 2 + 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 516 and 846 is 6
Notice that 6 = HCF(18,6) = HCF(42,18) = HCF(144,42) = HCF(186,144) = HCF(330,186) = HCF(516,330) = HCF(846,516) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 469 > 6, we apply the division lemma to 469 and 6, to get
469 = 6 x 78 + 1
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 1 and 6, to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 469 is 1
Notice that 1 = HCF(6,1) = HCF(469,6) .
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Frequently Asked Questions on HCF of 516, 846, 469 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 516, 846, 469?
Answer: HCF of 516, 846, 469 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 516, 846, 469 using Euclid's Algorithm?
Answer: For arbitrary numbers 516, 846, 469 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.