Highest Common Factor of 735, 521, 170 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 735, 521, 170 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 735, 521, 170 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 735, 521, 170 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 735, 521, 170 is 1.

HCF(735, 521, 170) = 1

HCF of 735, 521, 170 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 735, 521, 170 is 1.

Highest Common Factor of 735,521,170 using Euclid's algorithm

Highest Common Factor of 735,521,170 is 1

Step 1: Since 735 > 521, we apply the division lemma to 735 and 521, to get

735 = 521 x 1 + 214

Step 2: Since the reminder 521 ≠ 0, we apply division lemma to 214 and 521, to get

521 = 214 x 2 + 93

Step 3: We consider the new divisor 214 and the new remainder 93, and apply the division lemma to get

214 = 93 x 2 + 28

We consider the new divisor 93 and the new remainder 28,and apply the division lemma to get

93 = 28 x 3 + 9

We consider the new divisor 28 and the new remainder 9,and apply the division lemma to get

28 = 9 x 3 + 1

We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get

9 = 1 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 735 and 521 is 1

Notice that 1 = HCF(9,1) = HCF(28,9) = HCF(93,28) = HCF(214,93) = HCF(521,214) = HCF(735,521) .

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

Step 1: Since 170 > 1, we apply the division lemma to 170 and 1, to get

170 = 1 x 170 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 170 is 1

Notice that 1 = HCF(170,1) .

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Frequently Asked Questions on HCF of 735, 521, 170 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 735, 521, 170?

Answer: HCF of 735, 521, 170 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 735, 521, 170 using Euclid's Algorithm?

Answer: For arbitrary numbers 735, 521, 170 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.