Highest Common Factor of 267, 752, 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 267, 752, 169 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 267, 752, 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 267, 752, 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 267, 752, 169 is 1.

HCF(267, 752, 169) = 1

HCF of 267, 752, 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 267, 752, 169 is 1.

Highest Common Factor of 267,752,169 using Euclid's algorithm

Highest Common Factor of 267,752,169 is 1

Step 1: Since 752 > 267, we apply the division lemma to 752 and 267, to get

752 = 267 x 2 + 218

Step 2: Since the reminder 267 ≠ 0, we apply division lemma to 218 and 267, to get

267 = 218 x 1 + 49

Step 3: We consider the new divisor 218 and the new remainder 49, and apply the division lemma to get

218 = 49 x 4 + 22

We consider the new divisor 49 and the new remainder 22,and apply the division lemma to get

49 = 22 x 2 + 5

We consider the new divisor 22 and the new remainder 5,and apply the division lemma to get

22 = 5 x 4 + 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 267 and 752 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(22,5) = HCF(49,22) = HCF(218,49) = HCF(267,218) = HCF(752,267) .

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 267, 752, 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 267, 752, 169?

Answer: HCF of 267, 752, 169 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 267, 752, 169 using Euclid's Algorithm?

Answer: For arbitrary numbers 267, 752, 169 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.