Highest Common Factor of 464, 358, 133, 289 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 464, 358, 133, 289 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 464, 358, 133, 289 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 464, 358, 133, 289 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 464, 358, 133, 289 is 1.

HCF(464, 358, 133, 289) = 1

HCF of 464, 358, 133, 289 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 464, 358, 133, 289 is 1.

Highest Common Factor of 464,358,133,289 using Euclid's algorithm

Highest Common Factor of 464,358,133,289 is 1

Step 1: Since 464 > 358, we apply the division lemma to 464 and 358, to get

464 = 358 x 1 + 106

Step 2: Since the reminder 358 ≠ 0, we apply division lemma to 106 and 358, to get

358 = 106 x 3 + 40

Step 3: We consider the new divisor 106 and the new remainder 40, and apply the division lemma to get

106 = 40 x 2 + 26

We consider the new divisor 40 and the new remainder 26,and apply the division lemma to get

40 = 26 x 1 + 14

We consider the new divisor 26 and the new remainder 14,and apply the division lemma to get

26 = 14 x 1 + 12

We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get

14 = 12 x 1 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 464 and 358 is 2

Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(40,26) = HCF(106,40) = HCF(358,106) = HCF(464,358) .

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

Step 1: Since 133 > 2, we apply the division lemma to 133 and 2, to get

133 = 2 x 66 + 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 133 is 1

Notice that 1 = HCF(2,1) = HCF(133,2) .

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

Step 1: Since 289 > 1, we apply the division lemma to 289 and 1, to get

289 = 1 x 289 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 289 is 1

Notice that 1 = HCF(289,1) .

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Frequently Asked Questions on HCF of 464, 358, 133, 289 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 464, 358, 133, 289?

Answer: HCF of 464, 358, 133, 289 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 464, 358, 133, 289 using Euclid's Algorithm?

Answer: For arbitrary numbers 464, 358, 133, 289 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.