Highest Common Factor of 775, 975, 308 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, 975, 308 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 775, 975, 308 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, 975, 308 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, 975, 308 is 1.

HCF(775, 975, 308) = 1

HCF of 775, 975, 308 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, 975, 308 is 1.

Highest Common Factor of 775,975,308 using Euclid's algorithm

Highest Common Factor of 775,975,308 is 1

Step 1: Since 975 > 775, we apply the division lemma to 975 and 775, to get

975 = 775 x 1 + 200

Step 2: Since the reminder 775 ≠ 0, we apply division lemma to 200 and 775, to get

775 = 200 x 3 + 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 975 is 25

Notice that 25 = HCF(175,25) = HCF(200,175) = HCF(775,200) = HCF(975,775) .

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

Step 1: Since 308 > 25, we apply the division lemma to 308 and 25, to get

308 = 25 x 12 + 8

Step 2: Since the reminder 25 ≠ 0, we apply division lemma to 8 and 25, to get

25 = 8 x 3 + 1

Step 3: We consider the new divisor 8 and the new remainder 1, and apply the division lemma to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 25 and 308 is 1

Notice that 1 = HCF(8,1) = HCF(25,8) = HCF(308,25) .

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Frequently Asked Questions on HCF of 775, 975, 308 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, 975, 308?

Answer: HCF of 775, 975, 308 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 775, 975, 308 using Euclid's Algorithm?

Answer: For arbitrary numbers 775, 975, 308 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.