Highest Common Factor of 265, 735, 683, 25 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 265, 735, 683, 25 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 265, 735, 683, 25 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 265, 735, 683, 25 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 265, 735, 683, 25 is 1.

HCF(265, 735, 683, 25) = 1

HCF of 265, 735, 683, 25 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 265, 735, 683, 25 is 1.

Highest Common Factor of 265,735,683,25 using Euclid's algorithm

Highest Common Factor of 265,735,683,25 is 1

Step 1: Since 735 > 265, we apply the division lemma to 735 and 265, to get

735 = 265 x 2 + 205

Step 2: Since the reminder 265 ≠ 0, we apply division lemma to 205 and 265, to get

265 = 205 x 1 + 60

Step 3: We consider the new divisor 205 and the new remainder 60, and apply the division lemma to get

205 = 60 x 3 + 25

We consider the new divisor 60 and the new remainder 25,and apply the division lemma to get

60 = 25 x 2 + 10

We consider the new divisor 25 and the new remainder 10,and apply the division lemma to get

25 = 10 x 2 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 265 and 735 is 5

Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(60,25) = HCF(205,60) = HCF(265,205) = HCF(735,265) .

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

Step 1: Since 683 > 5, we apply the division lemma to 683 and 5, to get

683 = 5 x 136 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: 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 5 and 683 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(683,5) .

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

Step 1: Since 25 > 1, we apply the division lemma to 25 and 1, to get

25 = 1 x 25 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 25 is 1

Notice that 1 = HCF(25,1) .

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Frequently Asked Questions on HCF of 265, 735, 683, 25 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 265, 735, 683, 25?

Answer: HCF of 265, 735, 683, 25 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 265, 735, 683, 25 using Euclid's Algorithm?

Answer: For arbitrary numbers 265, 735, 683, 25 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.