Highest Common Factor of 936, 198, 310 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 936, 198, 310 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 936, 198, 310 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 936, 198, 310 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 936, 198, 310 is 2.

HCF(936, 198, 310) = 2

HCF of 936, 198, 310 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 936, 198, 310 is 2.

Highest Common Factor of 936,198,310 using Euclid's algorithm

Highest Common Factor of 936,198,310 is 2

Step 1: Since 936 > 198, we apply the division lemma to 936 and 198, to get

936 = 198 x 4 + 144

Step 2: Since the reminder 198 ≠ 0, we apply division lemma to 144 and 198, to get

198 = 144 x 1 + 54

Step 3: We consider the new divisor 144 and the new remainder 54, and apply the division lemma to get

144 = 54 x 2 + 36

We consider the new divisor 54 and the new remainder 36,and apply the division lemma to get

54 = 36 x 1 + 18

We consider the new divisor 36 and the new remainder 18,and apply the division lemma to get

36 = 18 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 936 and 198 is 18

Notice that 18 = HCF(36,18) = HCF(54,36) = HCF(144,54) = HCF(198,144) = HCF(936,198) .

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

Step 1: Since 310 > 18, we apply the division lemma to 310 and 18, to get

310 = 18 x 17 + 4

Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 4 and 18, to get

18 = 4 x 4 + 2

Step 3: 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 18 and 310 is 2

Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(310,18) .

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Frequently Asked Questions on HCF of 936, 198, 310 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 936, 198, 310?

Answer: HCF of 936, 198, 310 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 936, 198, 310 using Euclid's Algorithm?

Answer: For arbitrary numbers 936, 198, 310 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.