Highest Common Factor of 940, 560, 169 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 940, 560, 169 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 940, 560, 169 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 940, 560, 169 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 940, 560, 169 is 1.

HCF(940, 560, 169) = 1

HCF of 940, 560, 169 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 940, 560, 169 is 1.

Highest Common Factor of 940,560,169 using Euclid's algorithm

Highest Common Factor of 940,560,169 is 1

Step 1: Since 940 > 560, we apply the division lemma to 940 and 560, to get

940 = 560 x 1 + 380

Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 380 and 560, to get

560 = 380 x 1 + 180

Step 3: We consider the new divisor 380 and the new remainder 180, and apply the division lemma to get

380 = 180 x 2 + 20

We consider the new divisor 180 and the new remainder 20, and apply the division lemma to get

180 = 20 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 940 and 560 is 20

Notice that 20 = HCF(180,20) = HCF(380,180) = HCF(560,380) = HCF(940,560) .

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

Step 1: Since 169 > 20, we apply the division lemma to 169 and 20, to get

169 = 20 x 8 + 9

Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 9 and 20, to get

20 = 9 x 2 + 2

Step 3: We consider the new divisor 9 and the new remainder 2, and apply the division lemma to get

9 = 2 x 4 + 1

We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 20 and 169 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(20,9) = HCF(169,20) .

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Frequently Asked Questions on HCF of 940, 560, 169 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 940, 560, 169?

Answer: HCF of 940, 560, 169 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 940, 560, 169 using Euclid's Algorithm?

Answer: For arbitrary numbers 940, 560, 169 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.