Highest Common Factor of 750, 600, 238 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 750, 600, 238 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 750, 600, 238 is 2 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 750, 600, 238 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 750, 600, 238 is 2.

HCF(750, 600, 238) = 2

HCF of 750, 600, 238 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 750, 600, 238 is 2.

Highest Common Factor of 750,600,238 using Euclid's algorithm

Highest Common Factor of 750,600,238 is 2

Step 1: Since 750 > 600, we apply the division lemma to 750 and 600, to get

750 = 600 x 1 + 150

Step 2: Since the reminder 600 ≠ 0, we apply division lemma to 150 and 600, to get

600 = 150 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 150, the HCF of 750 and 600 is 150

Notice that 150 = HCF(600,150) = HCF(750,600) .

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

Step 1: Since 238 > 150, we apply the division lemma to 238 and 150, to get

238 = 150 x 1 + 88

Step 2: Since the reminder 150 ≠ 0, we apply division lemma to 88 and 150, to get

150 = 88 x 1 + 62

Step 3: We consider the new divisor 88 and the new remainder 62, and apply the division lemma to get

88 = 62 x 1 + 26

We consider the new divisor 62 and the new remainder 26,and apply the division lemma to get

62 = 26 x 2 + 10

We consider the new divisor 26 and the new remainder 10,and apply the division lemma to get

26 = 10 x 2 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 150 and 238 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(26,10) = HCF(62,26) = HCF(88,62) = HCF(150,88) = HCF(238,150) .

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Frequently Asked Questions on HCF of 750, 600, 238 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 750, 600, 238?

Answer: HCF of 750, 600, 238 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 750, 600, 238 using Euclid's Algorithm?

Answer: For arbitrary numbers 750, 600, 238 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.