Highest Common Factor of 378, 607 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 378, 607 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 378, 607 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 378, 607 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 378, 607 is 1.

HCF(378, 607) = 1

HCF of 378, 607 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 378, 607 is 1.

Highest Common Factor of 378,607 using Euclid's algorithm

Highest Common Factor of 378,607 is 1

Step 1: Since 607 > 378, we apply the division lemma to 607 and 378, to get

607 = 378 x 1 + 229

Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 229 and 378, to get

378 = 229 x 1 + 149

Step 3: We consider the new divisor 229 and the new remainder 149, and apply the division lemma to get

229 = 149 x 1 + 80

We consider the new divisor 149 and the new remainder 80,and apply the division lemma to get

149 = 80 x 1 + 69

We consider the new divisor 80 and the new remainder 69,and apply the division lemma to get

80 = 69 x 1 + 11

We consider the new divisor 69 and the new remainder 11,and apply the division lemma to get

69 = 11 x 6 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 2

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

3 = 2 x 1 + 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 378 and 607 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(69,11) = HCF(80,69) = HCF(149,80) = HCF(229,149) = HCF(378,229) = HCF(607,378) .

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Frequently Asked Questions on HCF of 378, 607 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 378, 607?

Answer: HCF of 378, 607 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 378, 607 using Euclid's Algorithm?

Answer: For arbitrary numbers 378, 607 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.