Highest Common Factor of 1606, 7875, 41607 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 1606, 7875, 41607 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1606, 7875, 41607 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 1606, 7875, 41607 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 1606, 7875, 41607 is 1.

HCF(1606, 7875, 41607) = 1

HCF of 1606, 7875, 41607 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 1606, 7875, 41607 is 1.

Highest Common Factor of 1606,7875,41607 using Euclid's algorithm

Highest Common Factor of 1606,7875,41607 is 1

Step 1: Since 7875 > 1606, we apply the division lemma to 7875 and 1606, to get

7875 = 1606 x 4 + 1451

Step 2: Since the reminder 1606 ≠ 0, we apply division lemma to 1451 and 1606, to get

1606 = 1451 x 1 + 155

Step 3: We consider the new divisor 1451 and the new remainder 155, and apply the division lemma to get

1451 = 155 x 9 + 56

We consider the new divisor 155 and the new remainder 56,and apply the division lemma to get

155 = 56 x 2 + 43

We consider the new divisor 56 and the new remainder 43,and apply the division lemma to get

56 = 43 x 1 + 13

We consider the new divisor 43 and the new remainder 13,and apply the division lemma to get

43 = 13 x 3 + 4

We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get

13 = 4 x 3 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1606 and 7875 is 1

Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(43,13) = HCF(56,43) = HCF(155,56) = HCF(1451,155) = HCF(1606,1451) = HCF(7875,1606) .

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

Step 1: Since 41607 > 1, we apply the division lemma to 41607 and 1, to get

41607 = 1 x 41607 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 41607 is 1

Notice that 1 = HCF(41607,1) .

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Frequently Asked Questions on HCF of 1606, 7875, 41607 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 1606, 7875, 41607?

Answer: HCF of 1606, 7875, 41607 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1606, 7875, 41607 using Euclid's Algorithm?

Answer: For arbitrary numbers 1606, 7875, 41607 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.