Highest Common Factor of 744, 221, 169 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 744, 221, 169 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 744, 221, 169 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 744, 221, 169 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 744, 221, 169 is 1.

HCF(744, 221, 169) = 1

HCF of 744, 221, 169 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 744, 221, 169 is 1.

Highest Common Factor of 744,221,169 using Euclid's algorithm

Highest Common Factor of 744,221,169 is 1

Step 1: Since 744 > 221, we apply the division lemma to 744 and 221, to get

744 = 221 x 3 + 81

Step 2: Since the reminder 221 ≠ 0, we apply division lemma to 81 and 221, to get

221 = 81 x 2 + 59

Step 3: We consider the new divisor 81 and the new remainder 59, and apply the division lemma to get

81 = 59 x 1 + 22

We consider the new divisor 59 and the new remainder 22,and apply the division lemma to get

59 = 22 x 2 + 15

We consider the new divisor 22 and the new remainder 15,and apply the division lemma to get

22 = 15 x 1 + 7

We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get

15 = 7 x 2 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 744 and 221 is 1

Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(22,15) = HCF(59,22) = HCF(81,59) = HCF(221,81) = HCF(744,221) .

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

Step 1: Since 169 > 1, we apply the division lemma to 169 and 1, to get

169 = 1 x 169 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 169 is 1

Notice that 1 = HCF(169,1) .

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Frequently Asked Questions on HCF of 744, 221, 169 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 744, 221, 169?

Answer: HCF of 744, 221, 169 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 744, 221, 169 using Euclid's Algorithm?

Answer: For arbitrary numbers 744, 221, 169 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.