Highest Common Factor of 405, 641, 154 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 405, 641, 154 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 405, 641, 154 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 405, 641, 154 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 405, 641, 154 is 1.

HCF(405, 641, 154) = 1

HCF of 405, 641, 154 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 405, 641, 154 is 1.

Highest Common Factor of 405,641,154 using Euclid's algorithm

Highest Common Factor of 405,641,154 is 1

Step 1: Since 641 > 405, we apply the division lemma to 641 and 405, to get

641 = 405 x 1 + 236

Step 2: Since the reminder 405 ≠ 0, we apply division lemma to 236 and 405, to get

405 = 236 x 1 + 169

Step 3: We consider the new divisor 236 and the new remainder 169, and apply the division lemma to get

236 = 169 x 1 + 67

We consider the new divisor 169 and the new remainder 67,and apply the division lemma to get

169 = 67 x 2 + 35

We consider the new divisor 67 and the new remainder 35,and apply the division lemma to get

67 = 35 x 1 + 32

We consider the new divisor 35 and the new remainder 32,and apply the division lemma to get

35 = 32 x 1 + 3

We consider the new divisor 32 and the new remainder 3,and apply the division lemma to get

32 = 3 x 10 + 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 405 and 641 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(32,3) = HCF(35,32) = HCF(67,35) = HCF(169,67) = HCF(236,169) = HCF(405,236) = HCF(641,405) .

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

Step 1: Since 154 > 1, we apply the division lemma to 154 and 1, to get

154 = 1 x 154 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 154 is 1

Notice that 1 = HCF(154,1) .

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Frequently Asked Questions on HCF of 405, 641, 154 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 405, 641, 154?

Answer: HCF of 405, 641, 154 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 405, 641, 154 using Euclid's Algorithm?

Answer: For arbitrary numbers 405, 641, 154 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.