Highest Common Factor of 562, 928, 754 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 562, 928, 754 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 562, 928, 754 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 562, 928, 754 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 562, 928, 754 is 2.

HCF(562, 928, 754) = 2

HCF of 562, 928, 754 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 562, 928, 754 is 2.

Highest Common Factor of 562,928,754 using Euclid's algorithm

Highest Common Factor of 562,928,754 is 2

Step 1: Since 928 > 562, we apply the division lemma to 928 and 562, to get

928 = 562 x 1 + 366

Step 2: Since the reminder 562 ≠ 0, we apply division lemma to 366 and 562, to get

562 = 366 x 1 + 196

Step 3: We consider the new divisor 366 and the new remainder 196, and apply the division lemma to get

366 = 196 x 1 + 170

We consider the new divisor 196 and the new remainder 170,and apply the division lemma to get

196 = 170 x 1 + 26

We consider the new divisor 170 and the new remainder 26,and apply the division lemma to get

170 = 26 x 6 + 14

We consider the new divisor 26 and the new remainder 14,and apply the division lemma to get

26 = 14 x 1 + 12

We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get

14 = 12 x 1 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 562 and 928 is 2

Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(170,26) = HCF(196,170) = HCF(366,196) = HCF(562,366) = HCF(928,562) .

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

Step 1: Since 754 > 2, we apply the division lemma to 754 and 2, to get

754 = 2 x 377 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 754 is 2

Notice that 2 = HCF(754,2) .

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Frequently Asked Questions on HCF of 562, 928, 754 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 562, 928, 754?

Answer: HCF of 562, 928, 754 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 562, 928, 754 using Euclid's Algorithm?

Answer: For arbitrary numbers 562, 928, 754 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.