Highest Common Factor of 112, 409, 463 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 112, 409, 463 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 112, 409, 463 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 112, 409, 463 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 112, 409, 463 is 1.

HCF(112, 409, 463) = 1

HCF of 112, 409, 463 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 112, 409, 463 is 1.

Highest Common Factor of 112,409,463 using Euclid's algorithm

Highest Common Factor of 112,409,463 is 1

Step 1: Since 409 > 112, we apply the division lemma to 409 and 112, to get

409 = 112 x 3 + 73

Step 2: Since the reminder 112 ≠ 0, we apply division lemma to 73 and 112, to get

112 = 73 x 1 + 39

Step 3: We consider the new divisor 73 and the new remainder 39, and apply the division lemma to get

73 = 39 x 1 + 34

We consider the new divisor 39 and the new remainder 34,and apply the division lemma to get

39 = 34 x 1 + 5

We consider the new divisor 34 and the new remainder 5,and apply the division lemma to get

34 = 5 x 6 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 112 and 409 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(34,5) = HCF(39,34) = HCF(73,39) = HCF(112,73) = HCF(409,112) .

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

Step 1: Since 463 > 1, we apply the division lemma to 463 and 1, to get

463 = 1 x 463 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 463 is 1

Notice that 1 = HCF(463,1) .

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Frequently Asked Questions on HCF of 112, 409, 463 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 112, 409, 463?

Answer: HCF of 112, 409, 463 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 112, 409, 463 using Euclid's Algorithm?

Answer: For arbitrary numbers 112, 409, 463 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.