Highest Common Factor of 880, 136, 309 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 880, 136, 309 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 880, 136, 309 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 880, 136, 309 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 880, 136, 309 is 1.

HCF(880, 136, 309) = 1

HCF of 880, 136, 309 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 880, 136, 309 is 1.

Highest Common Factor of 880,136,309 using Euclid's algorithm

Highest Common Factor of 880,136,309 is 1

Step 1: Since 880 > 136, we apply the division lemma to 880 and 136, to get

880 = 136 x 6 + 64

Step 2: Since the reminder 136 ≠ 0, we apply division lemma to 64 and 136, to get

136 = 64 x 2 + 8

Step 3: We consider the new divisor 64 and the new remainder 8, and apply the division lemma to get

64 = 8 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 880 and 136 is 8

Notice that 8 = HCF(64,8) = HCF(136,64) = HCF(880,136) .

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

Step 1: Since 309 > 8, we apply the division lemma to 309 and 8, to get

309 = 8 x 38 + 5

Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 5 and 8, to get

8 = 5 x 1 + 3

Step 3: We consider the new divisor 5 and the new remainder 3, and apply the division lemma to get

5 = 3 x 1 + 2

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

3 = 2 x 1 + 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 8 and 309 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(309,8) .

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Frequently Asked Questions on HCF of 880, 136, 309 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 880, 136, 309?

Answer: HCF of 880, 136, 309 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 880, 136, 309 using Euclid's Algorithm?

Answer: For arbitrary numbers 880, 136, 309 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.