Highest Common Factor of 884, 522, 574 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 884, 522, 574 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 884, 522, 574 is 2 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 884, 522, 574 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 884, 522, 574 is 2.

HCF(884, 522, 574) = 2

HCF of 884, 522, 574 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 884, 522, 574 is 2.

Highest Common Factor of 884,522,574 using Euclid's algorithm

Highest Common Factor of 884,522,574 is 2

Step 1: Since 884 > 522, we apply the division lemma to 884 and 522, to get

884 = 522 x 1 + 362

Step 2: Since the reminder 522 ≠ 0, we apply division lemma to 362 and 522, to get

522 = 362 x 1 + 160

Step 3: We consider the new divisor 362 and the new remainder 160, and apply the division lemma to get

362 = 160 x 2 + 42

We consider the new divisor 160 and the new remainder 42,and apply the division lemma to get

160 = 42 x 3 + 34

We consider the new divisor 42 and the new remainder 34,and apply the division lemma to get

42 = 34 x 1 + 8

We consider the new divisor 34 and the new remainder 8,and apply the division lemma to get

34 = 8 x 4 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 884 and 522 is 2

Notice that 2 = HCF(8,2) = HCF(34,8) = HCF(42,34) = HCF(160,42) = HCF(362,160) = HCF(522,362) = HCF(884,522) .

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

Step 1: Since 574 > 2, we apply the division lemma to 574 and 2, to get

574 = 2 x 287 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 574 is 2

Notice that 2 = HCF(574,2) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 884, 522, 574 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 884, 522, 574?

Answer: HCF of 884, 522, 574 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 884, 522, 574 using Euclid's Algorithm?

Answer: For arbitrary numbers 884, 522, 574 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.