Highest Common Factor of 372, 878, 179 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 372, 878, 179 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 372, 878, 179 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 372, 878, 179 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 372, 878, 179 is 1.

HCF(372, 878, 179) = 1

HCF of 372, 878, 179 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 372, 878, 179 is 1.

Highest Common Factor of 372,878,179 using Euclid's algorithm

Highest Common Factor of 372,878,179 is 1

Step 1: Since 878 > 372, we apply the division lemma to 878 and 372, to get

878 = 372 x 2 + 134

Step 2: Since the reminder 372 ≠ 0, we apply division lemma to 134 and 372, to get

372 = 134 x 2 + 104

Step 3: We consider the new divisor 134 and the new remainder 104, and apply the division lemma to get

134 = 104 x 1 + 30

We consider the new divisor 104 and the new remainder 30,and apply the division lemma to get

104 = 30 x 3 + 14

We consider the new divisor 30 and the new remainder 14,and apply the division lemma to get

30 = 14 x 2 + 2

We consider the new divisor 14 and the new remainder 2,and apply the division lemma 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 372 and 878 is 2

Notice that 2 = HCF(14,2) = HCF(30,14) = HCF(104,30) = HCF(134,104) = HCF(372,134) = HCF(878,372) .

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

Step 1: Since 179 > 2, we apply the division lemma to 179 and 2, to get

179 = 2 x 89 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 179 is 1

Notice that 1 = HCF(2,1) = HCF(179,2) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 372, 878, 179 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 372, 878, 179?

Answer: HCF of 372, 878, 179 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 372, 878, 179 using Euclid's Algorithm?

Answer: For arbitrary numbers 372, 878, 179 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.