Highest Common Factor of 135, 705, 527 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 135, 705, 527 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 135, 705, 527 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 135, 705, 527 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 135, 705, 527 is 1.

HCF(135, 705, 527) = 1

HCF of 135, 705, 527 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 135, 705, 527 is 1.

Highest Common Factor of 135,705,527 using Euclid's algorithm

Highest Common Factor of 135,705,527 is 1

Step 1: Since 705 > 135, we apply the division lemma to 705 and 135, to get

705 = 135 x 5 + 30

Step 2: Since the reminder 135 ≠ 0, we apply division lemma to 30 and 135, to get

135 = 30 x 4 + 15

Step 3: We consider the new divisor 30 and the new remainder 15, and apply the division lemma to get

30 = 15 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 135 and 705 is 15

Notice that 15 = HCF(30,15) = HCF(135,30) = HCF(705,135) .

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

Step 1: Since 527 > 15, we apply the division lemma to 527 and 15, to get

527 = 15 x 35 + 2

Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 2 and 15, to get

15 = 2 x 7 + 1

Step 3: 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 15 and 527 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(527,15) .

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Frequently Asked Questions on HCF of 135, 705, 527 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 135, 705, 527?

Answer: HCF of 135, 705, 527 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 135, 705, 527 using Euclid's Algorithm?

Answer: For arbitrary numbers 135, 705, 527 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.