Highest Common Factor of 875, 975, 348 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 875, 975, 348 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 875, 975, 348 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 875, 975, 348 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 875, 975, 348 is 1.

HCF(875, 975, 348) = 1

HCF of 875, 975, 348 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 875, 975, 348 is 1.

Highest Common Factor of 875,975,348 using Euclid's algorithm

Highest Common Factor of 875,975,348 is 1

Step 1: Since 975 > 875, we apply the division lemma to 975 and 875, to get

975 = 875 x 1 + 100

Step 2: Since the reminder 875 ≠ 0, we apply division lemma to 100 and 875, to get

875 = 100 x 8 + 75

Step 3: We consider the new divisor 100 and the new remainder 75, and apply the division lemma to get

100 = 75 x 1 + 25

We consider the new divisor 75 and the new remainder 25, and apply the division lemma to get

75 = 25 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 25, the HCF of 875 and 975 is 25

Notice that 25 = HCF(75,25) = HCF(100,75) = HCF(875,100) = HCF(975,875) .

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

Step 1: Since 348 > 25, we apply the division lemma to 348 and 25, to get

348 = 25 x 13 + 23

Step 2: Since the reminder 25 ≠ 0, we apply division lemma to 23 and 25, to get

25 = 23 x 1 + 2

Step 3: We consider the new divisor 23 and the new remainder 2, and apply the division lemma to get

23 = 2 x 11 + 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 25 and 348 is 1

Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(25,23) = HCF(348,25) .

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Frequently Asked Questions on HCF of 875, 975, 348 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 875, 975, 348?

Answer: HCF of 875, 975, 348 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 875, 975, 348 using Euclid's Algorithm?

Answer: For arbitrary numbers 875, 975, 348 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.