Highest Common Factor of 708, 874, 14 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 708, 874, 14 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 708, 874, 14 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 708, 874, 14 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 708, 874, 14 is 2.

HCF(708, 874, 14) = 2

HCF of 708, 874, 14 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 708, 874, 14 is 2.

Highest Common Factor of 708,874,14 using Euclid's algorithm

Highest Common Factor of 708,874,14 is 2

Step 1: Since 874 > 708, we apply the division lemma to 874 and 708, to get

874 = 708 x 1 + 166

Step 2: Since the reminder 708 ≠ 0, we apply division lemma to 166 and 708, to get

708 = 166 x 4 + 44

Step 3: We consider the new divisor 166 and the new remainder 44, and apply the division lemma to get

166 = 44 x 3 + 34

We consider the new divisor 44 and the new remainder 34,and apply the division lemma to get

44 = 34 x 1 + 10

We consider the new divisor 34 and the new remainder 10,and apply the division lemma to get

34 = 10 x 3 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 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 708 and 874 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(34,10) = HCF(44,34) = HCF(166,44) = HCF(708,166) = HCF(874,708) .

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

Step 1: Since 14 > 2, we apply the division lemma to 14 and 2, to get

14 = 2 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 14 is 2

Notice that 2 = HCF(14,2) .

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Frequently Asked Questions on HCF of 708, 874, 14 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 708, 874, 14?

Answer: HCF of 708, 874, 14 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 708, 874, 14 using Euclid's Algorithm?

Answer: For arbitrary numbers 708, 874, 14 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.