Highest Common Factor of 737, 310, 269 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 737, 310, 269 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 737, 310, 269 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 737, 310, 269 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 737, 310, 269 is 1.

HCF(737, 310, 269) = 1

HCF of 737, 310, 269 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 737, 310, 269 is 1.

Highest Common Factor of 737,310,269 using Euclid's algorithm

Highest Common Factor of 737,310,269 is 1

Step 1: Since 737 > 310, we apply the division lemma to 737 and 310, to get

737 = 310 x 2 + 117

Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 117 and 310, to get

310 = 117 x 2 + 76

Step 3: We consider the new divisor 117 and the new remainder 76, and apply the division lemma to get

117 = 76 x 1 + 41

We consider the new divisor 76 and the new remainder 41,and apply the division lemma to get

76 = 41 x 1 + 35

We consider the new divisor 41 and the new remainder 35,and apply the division lemma to get

41 = 35 x 1 + 6

We consider the new divisor 35 and the new remainder 6,and apply the division lemma to get

35 = 6 x 5 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 737 and 310 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(35,6) = HCF(41,35) = HCF(76,41) = HCF(117,76) = HCF(310,117) = HCF(737,310) .

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

Step 1: Since 269 > 1, we apply the division lemma to 269 and 1, to get

269 = 1 x 269 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 269 is 1

Notice that 1 = HCF(269,1) .

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Frequently Asked Questions on HCF of 737, 310, 269 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 737, 310, 269?

Answer: HCF of 737, 310, 269 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 737, 310, 269 using Euclid's Algorithm?

Answer: For arbitrary numbers 737, 310, 269 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.