Highest Common Factor of 906, 8524, 5460 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, 8524, 5460 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 906, 8524, 5460 is 2 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, 8524, 5460 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, 8524, 5460 is 2.
HCF(906, 8524, 5460) = 2
HCF of 906, 8524, 5460 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, 8524, 5460 is 2.
Highest Common Factor of 906,8524,5460 is 2
Step 1: Since 8524 > 906, we apply the division lemma to 8524 and 906, to get
8524 = 906 x 9 + 370
Step 2: Since the reminder 906 ≠ 0, we apply division lemma to 370 and 906, to get
906 = 370 x 2 + 166
Step 3: We consider the new divisor 370 and the new remainder 166, and apply the division lemma to get
370 = 166 x 2 + 38
We consider the new divisor 166 and the new remainder 38,and apply the division lemma to get
166 = 38 x 4 + 14
We consider the new divisor 38 and the new remainder 14,and apply the division lemma to get
38 = 14 x 2 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 906 and 8524 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(38,14) = HCF(166,38) = HCF(370,166) = HCF(906,370) = HCF(8524,906) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5460 > 2, we apply the division lemma to 5460 and 2, to get
5460 = 2 x 2730 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 5460 is 2
Notice that 2 = HCF(5460,2) .
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Frequently Asked Questions on HCF of 906, 8524, 5460 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, 8524, 5460?
Answer: HCF of 906, 8524, 5460 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 906, 8524, 5460 using Euclid's Algorithm?
Answer: For arbitrary numbers 906, 8524, 5460 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.