Highest Common Factor of 607, 767, 120 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 607, 767, 120 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 607, 767, 120 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 607, 767, 120 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 607, 767, 120 is 1.

HCF(607, 767, 120) = 1

HCF of 607, 767, 120 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 607, 767, 120 is 1.

Highest Common Factor of 607,767,120 using Euclid's algorithm

Highest Common Factor of 607,767,120 is 1

Step 1: Since 767 > 607, we apply the division lemma to 767 and 607, to get

767 = 607 x 1 + 160

Step 2: Since the reminder 607 ≠ 0, we apply division lemma to 160 and 607, to get

607 = 160 x 3 + 127

Step 3: We consider the new divisor 160 and the new remainder 127, and apply the division lemma to get

160 = 127 x 1 + 33

We consider the new divisor 127 and the new remainder 33,and apply the division lemma to get

127 = 33 x 3 + 28

We consider the new divisor 33 and the new remainder 28,and apply the division lemma to get

33 = 28 x 1 + 5

We consider the new divisor 28 and the new remainder 5,and apply the division lemma to get

28 = 5 x 5 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 607 and 767 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(28,5) = HCF(33,28) = HCF(127,33) = HCF(160,127) = HCF(607,160) = HCF(767,607) .

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

Step 1: Since 120 > 1, we apply the division lemma to 120 and 1, to get

120 = 1 x 120 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 120 is 1

Notice that 1 = HCF(120,1) .

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Frequently Asked Questions on HCF of 607, 767, 120 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 607, 767, 120?

Answer: HCF of 607, 767, 120 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 607, 767, 120 using Euclid's Algorithm?

Answer: For arbitrary numbers 607, 767, 120 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.