Highest Common Factor of 663, 945, 221 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 663, 945, 221 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 663, 945, 221 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 663, 945, 221 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 663, 945, 221 is 1.

HCF(663, 945, 221) = 1

HCF of 663, 945, 221 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 663, 945, 221 is 1.

Highest Common Factor of 663,945,221 using Euclid's algorithm

Highest Common Factor of 663,945,221 is 1

Step 1: Since 945 > 663, we apply the division lemma to 945 and 663, to get

945 = 663 x 1 + 282

Step 2: Since the reminder 663 ≠ 0, we apply division lemma to 282 and 663, to get

663 = 282 x 2 + 99

Step 3: We consider the new divisor 282 and the new remainder 99, and apply the division lemma to get

282 = 99 x 2 + 84

We consider the new divisor 99 and the new remainder 84,and apply the division lemma to get

99 = 84 x 1 + 15

We consider the new divisor 84 and the new remainder 15,and apply the division lemma to get

84 = 15 x 5 + 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 663 and 945 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(84,15) = HCF(99,84) = HCF(282,99) = HCF(663,282) = HCF(945,663) .

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

Step 1: Since 221 > 3, we apply the division lemma to 221 and 3, to get

221 = 3 x 73 + 2

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

3 = 2 x 1 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 221 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(221,3) .

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Frequently Asked Questions on HCF of 663, 945, 221 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 663, 945, 221?

Answer: HCF of 663, 945, 221 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 663, 945, 221 using Euclid's Algorithm?

Answer: For arbitrary numbers 663, 945, 221 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.