Highest Common Factor of 614, 235, 151 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 614, 235, 151 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 614, 235, 151 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 614, 235, 151 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 614, 235, 151 is 1.

HCF(614, 235, 151) = 1

HCF of 614, 235, 151 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 614, 235, 151 is 1.

Highest Common Factor of 614,235,151 using Euclid's algorithm

Highest Common Factor of 614,235,151 is 1

Step 1: Since 614 > 235, we apply the division lemma to 614 and 235, to get

614 = 235 x 2 + 144

Step 2: Since the reminder 235 ≠ 0, we apply division lemma to 144 and 235, to get

235 = 144 x 1 + 91

Step 3: We consider the new divisor 144 and the new remainder 91, and apply the division lemma to get

144 = 91 x 1 + 53

We consider the new divisor 91 and the new remainder 53,and apply the division lemma to get

91 = 53 x 1 + 38

We consider the new divisor 53 and the new remainder 38,and apply the division lemma to get

53 = 38 x 1 + 15

We consider the new divisor 38 and the new remainder 15,and apply the division lemma to get

38 = 15 x 2 + 8

We consider the new divisor 15 and the new remainder 8,and apply the division lemma to get

15 = 8 x 1 + 7

We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get

8 = 7 x 1 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 614 and 235 is 1

Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(15,8) = HCF(38,15) = HCF(53,38) = HCF(91,53) = HCF(144,91) = HCF(235,144) = HCF(614,235) .

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

Step 1: Since 151 > 1, we apply the division lemma to 151 and 1, to get

151 = 1 x 151 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 151 is 1

Notice that 1 = HCF(151,1) .

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Frequently Asked Questions on HCF of 614, 235, 151 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 614, 235, 151?

Answer: HCF of 614, 235, 151 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 614, 235, 151 using Euclid's Algorithm?

Answer: For arbitrary numbers 614, 235, 151 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.