Highest Common Factor of 874, 553 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 874, 553 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 874, 553 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 874, 553 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 874, 553 is 1.

HCF(874, 553) = 1

HCF of 874, 553 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 874, 553 is 1.

Highest Common Factor of 874,553 using Euclid's algorithm

Highest Common Factor of 874,553 is 1

Step 1: Since 874 > 553, we apply the division lemma to 874 and 553, to get

874 = 553 x 1 + 321

Step 2: Since the reminder 553 ≠ 0, we apply division lemma to 321 and 553, to get

553 = 321 x 1 + 232

Step 3: We consider the new divisor 321 and the new remainder 232, and apply the division lemma to get

321 = 232 x 1 + 89

We consider the new divisor 232 and the new remainder 89,and apply the division lemma to get

232 = 89 x 2 + 54

We consider the new divisor 89 and the new remainder 54,and apply the division lemma to get

89 = 54 x 1 + 35

We consider the new divisor 54 and the new remainder 35,and apply the division lemma to get

54 = 35 x 1 + 19

We consider the new divisor 35 and the new remainder 19,and apply the division lemma to get

35 = 19 x 1 + 16

We consider the new divisor 19 and the new remainder 16,and apply the division lemma to get

19 = 16 x 1 + 3

We consider the new divisor 16 and the new remainder 3,and apply the division lemma to get

16 = 3 x 5 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 874 and 553 is 1

Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(19,16) = HCF(35,19) = HCF(54,35) = HCF(89,54) = HCF(232,89) = HCF(321,232) = HCF(553,321) = HCF(874,553) .

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Frequently Asked Questions on HCF of 874, 553 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 874, 553?

Answer: HCF of 874, 553 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 874, 553 using Euclid's Algorithm?

Answer: For arbitrary numbers 874, 553 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.