Highest Common Factor of 367, 968, 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 367, 968, 169 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 367, 968, 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 367, 968, 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 367, 968, 169 is 1.

HCF(367, 968, 169) = 1

HCF of 367, 968, 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 367, 968, 169 is 1.

Highest Common Factor of 367,968,169 using Euclid's algorithm

Highest Common Factor of 367,968,169 is 1

Step 1: Since 968 > 367, we apply the division lemma to 968 and 367, to get

968 = 367 x 2 + 234

Step 2: Since the reminder 367 ≠ 0, we apply division lemma to 234 and 367, to get

367 = 234 x 1 + 133

Step 3: We consider the new divisor 234 and the new remainder 133, and apply the division lemma to get

234 = 133 x 1 + 101

We consider the new divisor 133 and the new remainder 101,and apply the division lemma to get

133 = 101 x 1 + 32

We consider the new divisor 101 and the new remainder 32,and apply the division lemma to get

101 = 32 x 3 + 5

We consider the new divisor 32 and the new remainder 5,and apply the division lemma to get

32 = 5 x 6 + 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 367 and 968 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(32,5) = HCF(101,32) = HCF(133,101) = HCF(234,133) = HCF(367,234) = HCF(968,367) .

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 367, 968, 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 367, 968, 169?

Answer: HCF of 367, 968, 169 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 367, 968, 169 using Euclid's Algorithm?

Answer: For arbitrary numbers 367, 968, 169 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.