Highest Common Factor of 354, 1606, 7663 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 354, 1606, 7663 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 354, 1606, 7663 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 354, 1606, 7663 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 354, 1606, 7663 is 1.

HCF(354, 1606, 7663) = 1

HCF of 354, 1606, 7663 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 354, 1606, 7663 is 1.

Highest Common Factor of 354,1606,7663 using Euclid's algorithm

Highest Common Factor of 354,1606,7663 is 1

Step 1: Since 1606 > 354, we apply the division lemma to 1606 and 354, to get

1606 = 354 x 4 + 190

Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 190 and 354, to get

354 = 190 x 1 + 164

Step 3: We consider the new divisor 190 and the new remainder 164, and apply the division lemma to get

190 = 164 x 1 + 26

We consider the new divisor 164 and the new remainder 26,and apply the division lemma to get

164 = 26 x 6 + 8

We consider the new divisor 26 and the new remainder 8,and apply the division lemma to get

26 = 8 x 3 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 354 and 1606 is 2

Notice that 2 = HCF(8,2) = HCF(26,8) = HCF(164,26) = HCF(190,164) = HCF(354,190) = HCF(1606,354) .

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

Step 1: Since 7663 > 2, we apply the division lemma to 7663 and 2, to get

7663 = 2 x 3831 + 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 7663 is 1

Notice that 1 = HCF(2,1) = HCF(7663,2) .

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Frequently Asked Questions on HCF of 354, 1606, 7663 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 354, 1606, 7663?

Answer: HCF of 354, 1606, 7663 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 354, 1606, 7663 using Euclid's Algorithm?

Answer: For arbitrary numbers 354, 1606, 7663 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.