Highest Common Factor of 542, 402, 465 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 542, 402, 465 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 542, 402, 465 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 542, 402, 465 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 542, 402, 465 is 1.

HCF(542, 402, 465) = 1

HCF of 542, 402, 465 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 542, 402, 465 is 1.

Highest Common Factor of 542,402,465 using Euclid's algorithm

Highest Common Factor of 542,402,465 is 1

Step 1: Since 542 > 402, we apply the division lemma to 542 and 402, to get

542 = 402 x 1 + 140

Step 2: Since the reminder 402 ≠ 0, we apply division lemma to 140 and 402, to get

402 = 140 x 2 + 122

Step 3: We consider the new divisor 140 and the new remainder 122, and apply the division lemma to get

140 = 122 x 1 + 18

We consider the new divisor 122 and the new remainder 18,and apply the division lemma to get

122 = 18 x 6 + 14

We consider the new divisor 18 and the new remainder 14,and apply the division lemma to get

18 = 14 x 1 + 4

We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get

14 = 4 x 3 + 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 542 and 402 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(122,18) = HCF(140,122) = HCF(402,140) = HCF(542,402) .

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

Step 1: Since 465 > 2, we apply the division lemma to 465 and 2, to get

465 = 2 x 232 + 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 465 is 1

Notice that 1 = HCF(2,1) = HCF(465,2) .

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Frequently Asked Questions on HCF of 542, 402, 465 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 542, 402, 465?

Answer: HCF of 542, 402, 465 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 542, 402, 465 using Euclid's Algorithm?

Answer: For arbitrary numbers 542, 402, 465 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.