Highest Common Factor of 562, 908, 509 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, 908, 509 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 562, 908, 509 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 562, 908, 509 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, 908, 509 is 1.

HCF(562, 908, 509) = 1

HCF of 562, 908, 509 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, 908, 509 is 1.

Highest Common Factor of 562,908,509 using Euclid's algorithm

Highest Common Factor of 562,908,509 is 1

Step 1: Since 908 > 562, we apply the division lemma to 908 and 562, to get

908 = 562 x 1 + 346

Step 2: Since the reminder 562 ≠ 0, we apply division lemma to 346 and 562, to get

562 = 346 x 1 + 216

Step 3: We consider the new divisor 346 and the new remainder 216, and apply the division lemma to get

346 = 216 x 1 + 130

We consider the new divisor 216 and the new remainder 130,and apply the division lemma to get

216 = 130 x 1 + 86

We consider the new divisor 130 and the new remainder 86,and apply the division lemma to get

130 = 86 x 1 + 44

We consider the new divisor 86 and the new remainder 44,and apply the division lemma to get

86 = 44 x 1 + 42

We consider the new divisor 44 and the new remainder 42,and apply the division lemma to get

44 = 42 x 1 + 2

We consider the new divisor 42 and the new remainder 2,and apply the division lemma to get

42 = 2 x 21 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 562 and 908 is 2

Notice that 2 = HCF(42,2) = HCF(44,42) = HCF(86,44) = HCF(130,86) = HCF(216,130) = HCF(346,216) = HCF(562,346) = HCF(908,562) .

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

Step 1: Since 509 > 2, we apply the division lemma to 509 and 2, to get

509 = 2 x 254 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 509 is 1

Notice that 1 = HCF(2,1) = HCF(509,2) .

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Frequently Asked Questions on HCF of 562, 908, 509 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, 908, 509?

Answer: HCF of 562, 908, 509 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 562, 908, 509 using Euclid's Algorithm?

Answer: For arbitrary numbers 562, 908, 509 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.