Highest Common Factor of 786, 478, 375 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 786, 478, 375 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 786, 478, 375 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 786, 478, 375 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 786, 478, 375 is 1.

HCF(786, 478, 375) = 1

HCF of 786, 478, 375 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 786, 478, 375 is 1.

Highest Common Factor of 786,478,375 using Euclid's algorithm

Highest Common Factor of 786,478,375 is 1

Step 1: Since 786 > 478, we apply the division lemma to 786 and 478, to get

786 = 478 x 1 + 308

Step 2: Since the reminder 478 ≠ 0, we apply division lemma to 308 and 478, to get

478 = 308 x 1 + 170

Step 3: We consider the new divisor 308 and the new remainder 170, and apply the division lemma to get

308 = 170 x 1 + 138

We consider the new divisor 170 and the new remainder 138,and apply the division lemma to get

170 = 138 x 1 + 32

We consider the new divisor 138 and the new remainder 32,and apply the division lemma to get

138 = 32 x 4 + 10

We consider the new divisor 32 and the new remainder 10,and apply the division lemma to get

32 = 10 x 3 + 2

We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get

10 = 2 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 786 and 478 is 2

Notice that 2 = HCF(10,2) = HCF(32,10) = HCF(138,32) = HCF(170,138) = HCF(308,170) = HCF(478,308) = HCF(786,478) .

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

Step 1: Since 375 > 2, we apply the division lemma to 375 and 2, to get

375 = 2 x 187 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 375 is 1

Notice that 1 = HCF(2,1) = HCF(375,2) .

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Frequently Asked Questions on HCF of 786, 478, 375 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 786, 478, 375?

Answer: HCF of 786, 478, 375 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 786, 478, 375 using Euclid's Algorithm?

Answer: For arbitrary numbers 786, 478, 375 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.