Highest Common Factor of 560, 972, 499 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 560, 972, 499 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 560, 972, 499 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 560, 972, 499 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 560, 972, 499 is 1.

HCF(560, 972, 499) = 1

HCF of 560, 972, 499 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 560, 972, 499 is 1.

Highest Common Factor of 560,972,499 using Euclid's algorithm

Highest Common Factor of 560,972,499 is 1

Step 1: Since 972 > 560, we apply the division lemma to 972 and 560, to get

972 = 560 x 1 + 412

Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 412 and 560, to get

560 = 412 x 1 + 148

Step 3: We consider the new divisor 412 and the new remainder 148, and apply the division lemma to get

412 = 148 x 2 + 116

We consider the new divisor 148 and the new remainder 116,and apply the division lemma to get

148 = 116 x 1 + 32

We consider the new divisor 116 and the new remainder 32,and apply the division lemma to get

116 = 32 x 3 + 20

We consider the new divisor 32 and the new remainder 20,and apply the division lemma to get

32 = 20 x 1 + 12

We consider the new divisor 20 and the new remainder 12,and apply the division lemma to get

20 = 12 x 1 + 8

We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get

12 = 8 x 1 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 560 and 972 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(32,20) = HCF(116,32) = HCF(148,116) = HCF(412,148) = HCF(560,412) = HCF(972,560) .

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

Step 1: Since 499 > 4, we apply the division lemma to 499 and 4, to get

499 = 4 x 124 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: 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 4 and 499 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(499,4) .

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Frequently Asked Questions on HCF of 560, 972, 499 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 560, 972, 499?

Answer: HCF of 560, 972, 499 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 560, 972, 499 using Euclid's Algorithm?

Answer: For arbitrary numbers 560, 972, 499 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.