Highest Common Factor of 256, 416, 229 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 256, 416, 229 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 256, 416, 229 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 256, 416, 229 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 256, 416, 229 is 1.

HCF(256, 416, 229) = 1

HCF of 256, 416, 229 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 256, 416, 229 is 1.

Highest Common Factor of 256,416,229 using Euclid's algorithm

Highest Common Factor of 256,416,229 is 1

Step 1: Since 416 > 256, we apply the division lemma to 416 and 256, to get

416 = 256 x 1 + 160

Step 2: Since the reminder 256 ≠ 0, we apply division lemma to 160 and 256, to get

256 = 160 x 1 + 96

Step 3: We consider the new divisor 160 and the new remainder 96, and apply the division lemma to get

160 = 96 x 1 + 64

We consider the new divisor 96 and the new remainder 64,and apply the division lemma to get

96 = 64 x 1 + 32

We consider the new divisor 64 and the new remainder 32,and apply the division lemma to get

64 = 32 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 256 and 416 is 32

Notice that 32 = HCF(64,32) = HCF(96,64) = HCF(160,96) = HCF(256,160) = HCF(416,256) .

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

Step 1: Since 229 > 32, we apply the division lemma to 229 and 32, to get

229 = 32 x 7 + 5

Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 5 and 32, to get

32 = 5 x 6 + 2

Step 3: We consider the new divisor 5 and the new remainder 2, and apply the division lemma to get

5 = 2 x 2 + 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 32 and 229 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(32,5) = HCF(229,32) .

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Frequently Asked Questions on HCF of 256, 416, 229 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 256, 416, 229?

Answer: HCF of 256, 416, 229 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 256, 416, 229 using Euclid's Algorithm?

Answer: For arbitrary numbers 256, 416, 229 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.