Highest Common Factor of 180, 864, 416 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 180, 864, 416 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 180, 864, 416 is 4 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 180, 864, 416 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 180, 864, 416 is 4.

HCF(180, 864, 416) = 4

HCF of 180, 864, 416 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 180, 864, 416 is 4.

Highest Common Factor of 180,864,416 using Euclid's algorithm

Highest Common Factor of 180,864,416 is 4

Step 1: Since 864 > 180, we apply the division lemma to 864 and 180, to get

864 = 180 x 4 + 144

Step 2: Since the reminder 180 ≠ 0, we apply division lemma to 144 and 180, to get

180 = 144 x 1 + 36

Step 3: We consider the new divisor 144 and the new remainder 36, and apply the division lemma to get

144 = 36 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 36, the HCF of 180 and 864 is 36

Notice that 36 = HCF(144,36) = HCF(180,144) = HCF(864,180) .

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

Step 1: Since 416 > 36, we apply the division lemma to 416 and 36, to get

416 = 36 x 11 + 20

Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 20 and 36, to get

36 = 20 x 1 + 16

Step 3: We consider the new divisor 20 and the new remainder 16, and apply the division lemma to get

20 = 16 x 1 + 4

We consider the new divisor 16 and the new remainder 4, and apply the division lemma to get

16 = 4 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 36 and 416 is 4

Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(36,20) = HCF(416,36) .

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Frequently Asked Questions on HCF of 180, 864, 416 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 180, 864, 416?

Answer: HCF of 180, 864, 416 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 180, 864, 416 using Euclid's Algorithm?

Answer: For arbitrary numbers 180, 864, 416 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.