Highest Common Factor of 401, 658, 56 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 401, 658, 56 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 401, 658, 56 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 401, 658, 56 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 401, 658, 56 is 1.

HCF(401, 658, 56) = 1

HCF of 401, 658, 56 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 401, 658, 56 is 1.

Highest Common Factor of 401,658,56 using Euclid's algorithm

Highest Common Factor of 401,658,56 is 1

Step 1: Since 658 > 401, we apply the division lemma to 658 and 401, to get

658 = 401 x 1 + 257

Step 2: Since the reminder 401 ≠ 0, we apply division lemma to 257 and 401, to get

401 = 257 x 1 + 144

Step 3: We consider the new divisor 257 and the new remainder 144, and apply the division lemma to get

257 = 144 x 1 + 113

We consider the new divisor 144 and the new remainder 113,and apply the division lemma to get

144 = 113 x 1 + 31

We consider the new divisor 113 and the new remainder 31,and apply the division lemma to get

113 = 31 x 3 + 20

We consider the new divisor 31 and the new remainder 20,and apply the division lemma to get

31 = 20 x 1 + 11

We consider the new divisor 20 and the new remainder 11,and apply the division lemma to get

20 = 11 x 1 + 9

We consider the new divisor 11 and the new remainder 9,and apply the division lemma to get

11 = 9 x 1 + 2

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 401 and 658 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(20,11) = HCF(31,20) = HCF(113,31) = HCF(144,113) = HCF(257,144) = HCF(401,257) = HCF(658,401) .

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

Step 1: Since 56 > 1, we apply the division lemma to 56 and 1, to get

56 = 1 x 56 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 56 is 1

Notice that 1 = HCF(56,1) .

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Frequently Asked Questions on HCF of 401, 658, 56 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 401, 658, 56?

Answer: HCF of 401, 658, 56 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 401, 658, 56 using Euclid's Algorithm?

Answer: For arbitrary numbers 401, 658, 56 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.