Highest Common Factor of 158, 414, 455 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 158, 414, 455 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 158, 414, 455 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 158, 414, 455 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 158, 414, 455 is 1.

HCF(158, 414, 455) = 1

HCF of 158, 414, 455 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 158, 414, 455 is 1.

Highest Common Factor of 158,414,455 using Euclid's algorithm

Highest Common Factor of 158,414,455 is 1

Step 1: Since 414 > 158, we apply the division lemma to 414 and 158, to get

414 = 158 x 2 + 98

Step 2: Since the reminder 158 ≠ 0, we apply division lemma to 98 and 158, to get

158 = 98 x 1 + 60

Step 3: We consider the new divisor 98 and the new remainder 60, and apply the division lemma to get

98 = 60 x 1 + 38

We consider the new divisor 60 and the new remainder 38,and apply the division lemma to get

60 = 38 x 1 + 22

We consider the new divisor 38 and the new remainder 22,and apply the division lemma to get

38 = 22 x 1 + 16

We consider the new divisor 22 and the new remainder 16,and apply the division lemma to get

22 = 16 x 1 + 6

We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get

16 = 6 x 2 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 158 and 414 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(38,22) = HCF(60,38) = HCF(98,60) = HCF(158,98) = HCF(414,158) .

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

Step 1: Since 455 > 2, we apply the division lemma to 455 and 2, to get

455 = 2 x 227 + 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 455 is 1

Notice that 1 = HCF(2,1) = HCF(455,2) .

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Frequently Asked Questions on HCF of 158, 414, 455 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 158, 414, 455?

Answer: HCF of 158, 414, 455 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 158, 414, 455 using Euclid's Algorithm?

Answer: For arbitrary numbers 158, 414, 455 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.