Highest Common Factor of 742, 313, 118 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 742, 313, 118 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 742, 313, 118 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 742, 313, 118 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 742, 313, 118 is 1.

HCF(742, 313, 118) = 1

HCF of 742, 313, 118 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 742, 313, 118 is 1.

Highest Common Factor of 742,313,118 using Euclid's algorithm

Highest Common Factor of 742,313,118 is 1

Step 1: Since 742 > 313, we apply the division lemma to 742 and 313, to get

742 = 313 x 2 + 116

Step 2: Since the reminder 313 ≠ 0, we apply division lemma to 116 and 313, to get

313 = 116 x 2 + 81

Step 3: We consider the new divisor 116 and the new remainder 81, and apply the division lemma to get

116 = 81 x 1 + 35

We consider the new divisor 81 and the new remainder 35,and apply the division lemma to get

81 = 35 x 2 + 11

We consider the new divisor 35 and the new remainder 11,and apply the division lemma to get

35 = 11 x 3 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 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 742 and 313 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(35,11) = HCF(81,35) = HCF(116,81) = HCF(313,116) = HCF(742,313) .

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

Step 1: Since 118 > 1, we apply the division lemma to 118 and 1, to get

118 = 1 x 118 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 118 is 1

Notice that 1 = HCF(118,1) .

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Frequently Asked Questions on HCF of 742, 313, 118 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 742, 313, 118?

Answer: HCF of 742, 313, 118 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 742, 313, 118 using Euclid's Algorithm?

Answer: For arbitrary numbers 742, 313, 118 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.