Highest Common Factor of 900, 9669, 6292 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 900, 9669, 6292 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 900, 9669, 6292 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 900, 9669, 6292 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 900, 9669, 6292 is 1.

HCF(900, 9669, 6292) = 1

HCF of 900, 9669, 6292 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 900, 9669, 6292 is 1.

Highest Common Factor of 900,9669,6292 using Euclid's algorithm

Highest Common Factor of 900,9669,6292 is 1

Step 1: Since 9669 > 900, we apply the division lemma to 9669 and 900, to get

9669 = 900 x 10 + 669

Step 2: Since the reminder 900 ≠ 0, we apply division lemma to 669 and 900, to get

900 = 669 x 1 + 231

Step 3: We consider the new divisor 669 and the new remainder 231, and apply the division lemma to get

669 = 231 x 2 + 207

We consider the new divisor 231 and the new remainder 207,and apply the division lemma to get

231 = 207 x 1 + 24

We consider the new divisor 207 and the new remainder 24,and apply the division lemma to get

207 = 24 x 8 + 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 900 and 9669 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(24,15) = HCF(207,24) = HCF(231,207) = HCF(669,231) = HCF(900,669) = HCF(9669,900) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 6292 > 3, we apply the division lemma to 6292 and 3, to get

6292 = 3 x 2097 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 6292 is 1

Notice that 1 = HCF(3,1) = HCF(6292,3) .

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Frequently Asked Questions on HCF of 900, 9669, 6292 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 900, 9669, 6292?

Answer: HCF of 900, 9669, 6292 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 900, 9669, 6292 using Euclid's Algorithm?

Answer: For arbitrary numbers 900, 9669, 6292 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.