Highest Common Factor of 906, 513, 849 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 906, 513, 849 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 906, 513, 849 is 3 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 906, 513, 849 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 906, 513, 849 is 3.
HCF(906, 513, 849) = 3
HCF of 906, 513, 849 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 906, 513, 849 is 3.
Highest Common Factor of 906,513,849 is 3
Step 1: Since 906 > 513, we apply the division lemma to 906 and 513, to get
906 = 513 x 1 + 393
Step 2: Since the reminder 513 ≠ 0, we apply division lemma to 393 and 513, to get
513 = 393 x 1 + 120
Step 3: We consider the new divisor 393 and the new remainder 120, and apply the division lemma to get
393 = 120 x 3 + 33
We consider the new divisor 120 and the new remainder 33,and apply the division lemma to get
120 = 33 x 3 + 21
We consider the new divisor 33 and the new remainder 21,and apply the division lemma to get
33 = 21 x 1 + 12
We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 906 and 513 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(33,21) = HCF(120,33) = HCF(393,120) = HCF(513,393) = HCF(906,513) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 849 > 3, we apply the division lemma to 849 and 3, to get
849 = 3 x 283 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 849 is 3
Notice that 3 = HCF(849,3) .
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Frequently Asked Questions on HCF of 906, 513, 849 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 906, 513, 849?
Answer: HCF of 906, 513, 849 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 906, 513, 849 using Euclid's Algorithm?
Answer: For arbitrary numbers 906, 513, 849 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.