Highest Common Factor of 600, 925, 148 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 600, 925, 148 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 600, 925, 148 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 600, 925, 148 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 600, 925, 148 is 1.

HCF(600, 925, 148) = 1

HCF of 600, 925, 148 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 600, 925, 148 is 1.

Highest Common Factor of 600,925,148 using Euclid's algorithm

Highest Common Factor of 600,925,148 is 1

Step 1: Since 925 > 600, we apply the division lemma to 925 and 600, to get

925 = 600 x 1 + 325

Step 2: Since the reminder 600 ≠ 0, we apply division lemma to 325 and 600, to get

600 = 325 x 1 + 275

Step 3: We consider the new divisor 325 and the new remainder 275, and apply the division lemma to get

325 = 275 x 1 + 50

We consider the new divisor 275 and the new remainder 50,and apply the division lemma to get

275 = 50 x 5 + 25

We consider the new divisor 50 and the new remainder 25,and apply the division lemma to get

50 = 25 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 25, the HCF of 600 and 925 is 25

Notice that 25 = HCF(50,25) = HCF(275,50) = HCF(325,275) = HCF(600,325) = HCF(925,600) .

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

Step 1: Since 148 > 25, we apply the division lemma to 148 and 25, to get

148 = 25 x 5 + 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 148 is 1

Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(25,23) = HCF(148,25) .

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Frequently Asked Questions on HCF of 600, 925, 148 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 600, 925, 148?

Answer: HCF of 600, 925, 148 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 600, 925, 148 using Euclid's Algorithm?

Answer: For arbitrary numbers 600, 925, 148 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.