Highest Common Factor of 223, 121, 966 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 223, 121, 966 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 223, 121, 966 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 223, 121, 966 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 223, 121, 966 is 1.

HCF(223, 121, 966) = 1

HCF of 223, 121, 966 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 223, 121, 966 is 1.

Highest Common Factor of 223,121,966 using Euclid's algorithm

Highest Common Factor of 223,121,966 is 1

Step 1: Since 223 > 121, we apply the division lemma to 223 and 121, to get

223 = 121 x 1 + 102

Step 2: Since the reminder 121 ≠ 0, we apply division lemma to 102 and 121, to get

121 = 102 x 1 + 19

Step 3: We consider the new divisor 102 and the new remainder 19, and apply the division lemma to get

102 = 19 x 5 + 7

We consider the new divisor 19 and the new remainder 7,and apply the division lemma to get

19 = 7 x 2 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 1

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 223 and 121 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(19,7) = HCF(102,19) = HCF(121,102) = HCF(223,121) .

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

Step 1: Since 966 > 1, we apply the division lemma to 966 and 1, to get

966 = 1 x 966 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 966 is 1

Notice that 1 = HCF(966,1) .

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Frequently Asked Questions on HCF of 223, 121, 966 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 223, 121, 966?

Answer: HCF of 223, 121, 966 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 223, 121, 966 using Euclid's Algorithm?

Answer: For arbitrary numbers 223, 121, 966 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.