Highest Common Factor of 156, 533, 138 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 156, 533, 138 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 156, 533, 138 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 156, 533, 138 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 156, 533, 138 is 1.

HCF(156, 533, 138) = 1

HCF of 156, 533, 138 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 156, 533, 138 is 1.

Highest Common Factor of 156,533,138 using Euclid's algorithm

Highest Common Factor of 156,533,138 is 1

Step 1: Since 533 > 156, we apply the division lemma to 533 and 156, to get

533 = 156 x 3 + 65

Step 2: Since the reminder 156 ≠ 0, we apply division lemma to 65 and 156, to get

156 = 65 x 2 + 26

Step 3: We consider the new divisor 65 and the new remainder 26, and apply the division lemma to get

65 = 26 x 2 + 13

We consider the new divisor 26 and the new remainder 13, and apply the division lemma to get

26 = 13 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 156 and 533 is 13

Notice that 13 = HCF(26,13) = HCF(65,26) = HCF(156,65) = HCF(533,156) .

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

Step 1: Since 138 > 13, we apply the division lemma to 138 and 13, to get

138 = 13 x 10 + 8

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 8 and 13, to get

13 = 8 x 1 + 5

Step 3: We consider the new divisor 8 and the new remainder 5, and apply the division lemma to get

8 = 5 x 1 + 3

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

5 = 3 x 1 + 2

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

3 = 2 x 1 + 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 13 and 138 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(138,13) .

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Frequently Asked Questions on HCF of 156, 533, 138 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 156, 533, 138?

Answer: HCF of 156, 533, 138 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 156, 533, 138 using Euclid's Algorithm?

Answer: For arbitrary numbers 156, 533, 138 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.