Highest Common Factor of 254, 416, 984 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 254, 416, 984 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 254, 416, 984 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 254, 416, 984 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 254, 416, 984 is 2.

HCF(254, 416, 984) = 2

HCF of 254, 416, 984 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 254, 416, 984 is 2.

Highest Common Factor of 254,416,984 using Euclid's algorithm

Highest Common Factor of 254,416,984 is 2

Step 1: Since 416 > 254, we apply the division lemma to 416 and 254, to get

416 = 254 x 1 + 162

Step 2: Since the reminder 254 ≠ 0, we apply division lemma to 162 and 254, to get

254 = 162 x 1 + 92

Step 3: We consider the new divisor 162 and the new remainder 92, and apply the division lemma to get

162 = 92 x 1 + 70

We consider the new divisor 92 and the new remainder 70,and apply the division lemma to get

92 = 70 x 1 + 22

We consider the new divisor 70 and the new remainder 22,and apply the division lemma to get

70 = 22 x 3 + 4

We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get

22 = 4 x 5 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 254 and 416 is 2

Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(70,22) = HCF(92,70) = HCF(162,92) = HCF(254,162) = HCF(416,254) .

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

Step 1: Since 984 > 2, we apply the division lemma to 984 and 2, to get

984 = 2 x 492 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 984 is 2

Notice that 2 = HCF(984,2) .

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Frequently Asked Questions on HCF of 254, 416, 984 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 254, 416, 984?

Answer: HCF of 254, 416, 984 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 254, 416, 984 using Euclid's Algorithm?

Answer: For arbitrary numbers 254, 416, 984 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.