Highest Common Factor of 775, 575, 338 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 775, 575, 338 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 775, 575, 338 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 775, 575, 338 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 775, 575, 338 is 1.

HCF(775, 575, 338) = 1

HCF of 775, 575, 338 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 775, 575, 338 is 1.

Highest Common Factor of 775,575,338 using Euclid's algorithm

Highest Common Factor of 775,575,338 is 1

Step 1: Since 775 > 575, we apply the division lemma to 775 and 575, to get

775 = 575 x 1 + 200

Step 2: Since the reminder 575 ≠ 0, we apply division lemma to 200 and 575, to get

575 = 200 x 2 + 175

Step 3: We consider the new divisor 200 and the new remainder 175, and apply the division lemma to get

200 = 175 x 1 + 25

We consider the new divisor 175 and the new remainder 25, and apply the division lemma to get

175 = 25 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 25, the HCF of 775 and 575 is 25

Notice that 25 = HCF(175,25) = HCF(200,175) = HCF(575,200) = HCF(775,575) .

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

Step 1: Since 338 > 25, we apply the division lemma to 338 and 25, to get

338 = 25 x 13 + 13

Step 2: Since the reminder 25 ≠ 0, we apply division lemma to 13 and 25, to get

25 = 13 x 1 + 12

Step 3: We consider the new divisor 13 and the new remainder 12, and apply the division lemma to get

13 = 12 x 1 + 1

We consider the new divisor 12 and the new remainder 1, and apply the division lemma to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 25 and 338 is 1

Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(25,13) = HCF(338,25) .

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Frequently Asked Questions on HCF of 775, 575, 338 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 775, 575, 338?

Answer: HCF of 775, 575, 338 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 775, 575, 338 using Euclid's Algorithm?

Answer: For arbitrary numbers 775, 575, 338 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.