Highest Common Factor of 675, 405, 906 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 675, 405, 906 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 675, 405, 906 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 675, 405, 906 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 675, 405, 906 is 3.
HCF(675, 405, 906) = 3
HCF of 675, 405, 906 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 675, 405, 906 is 3.
Highest Common Factor of 675,405,906 is 3
Step 1: Since 675 > 405, we apply the division lemma to 675 and 405, to get
675 = 405 x 1 + 270
Step 2: Since the reminder 405 ≠ 0, we apply division lemma to 270 and 405, to get
405 = 270 x 1 + 135
Step 3: We consider the new divisor 270 and the new remainder 135, and apply the division lemma to get
270 = 135 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 135, the HCF of 675 and 405 is 135
Notice that 135 = HCF(270,135) = HCF(405,270) = HCF(675,405) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 906 > 135, we apply the division lemma to 906 and 135, to get
906 = 135 x 6 + 96
Step 2: Since the reminder 135 ≠ 0, we apply division lemma to 96 and 135, to get
135 = 96 x 1 + 39
Step 3: We consider the new divisor 96 and the new remainder 39, and apply the division lemma to get
96 = 39 x 2 + 18
We consider the new divisor 39 and the new remainder 18,and apply the division lemma to get
39 = 18 x 2 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 135 and 906 is 3
Notice that 3 = HCF(18,3) = HCF(39,18) = HCF(96,39) = HCF(135,96) = HCF(906,135) .
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Frequently Asked Questions on HCF of 675, 405, 906 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 675, 405, 906?
Answer: HCF of 675, 405, 906 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 675, 405, 906 using Euclid's Algorithm?
Answer: For arbitrary numbers 675, 405, 906 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.