Highest Common Factor of 512, 905, 669, 258 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 512, 905, 669, 258 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 512, 905, 669, 258 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 512, 905, 669, 258 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 512, 905, 669, 258 is 1.

HCF(512, 905, 669, 258) = 1

HCF of 512, 905, 669, 258 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 512, 905, 669, 258 is 1.

Highest Common Factor of 512,905,669,258 using Euclid's algorithm

Highest Common Factor of 512,905,669,258 is 1

Step 1: Since 905 > 512, we apply the division lemma to 905 and 512, to get

905 = 512 x 1 + 393

Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 393 and 512, to get

512 = 393 x 1 + 119

Step 3: We consider the new divisor 393 and the new remainder 119, and apply the division lemma to get

393 = 119 x 3 + 36

We consider the new divisor 119 and the new remainder 36,and apply the division lemma to get

119 = 36 x 3 + 11

We consider the new divisor 36 and the new remainder 11,and apply the division lemma to get

36 = 11 x 3 + 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 512 and 905 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(36,11) = HCF(119,36) = HCF(393,119) = HCF(512,393) = HCF(905,512) .

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

Step 1: Since 669 > 1, we apply the division lemma to 669 and 1, to get

669 = 1 x 669 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 669 is 1

Notice that 1 = HCF(669,1) .

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

Step 1: Since 258 > 1, we apply the division lemma to 258 and 1, to get

258 = 1 x 258 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 258 is 1

Notice that 1 = HCF(258,1) .

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Frequently Asked Questions on HCF of 512, 905, 669, 258 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 512, 905, 669, 258?

Answer: HCF of 512, 905, 669, 258 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 512, 905, 669, 258 using Euclid's Algorithm?

Answer: For arbitrary numbers 512, 905, 669, 258 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.