Highest Common Factor of 312, 896, 457, 188 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 312, 896, 457, 188 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 312, 896, 457, 188 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 312, 896, 457, 188 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 312, 896, 457, 188 is 1.

HCF(312, 896, 457, 188) = 1

HCF of 312, 896, 457, 188 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 312, 896, 457, 188 is 1.

Highest Common Factor of 312,896,457,188 using Euclid's algorithm

Highest Common Factor of 312,896,457,188 is 1

Step 1: Since 896 > 312, we apply the division lemma to 896 and 312, to get

896 = 312 x 2 + 272

Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 272 and 312, to get

312 = 272 x 1 + 40

Step 3: We consider the new divisor 272 and the new remainder 40, and apply the division lemma to get

272 = 40 x 6 + 32

We consider the new divisor 40 and the new remainder 32,and apply the division lemma to get

40 = 32 x 1 + 8

We consider the new divisor 32 and the new remainder 8,and apply the division lemma to get

32 = 8 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 312 and 896 is 8

Notice that 8 = HCF(32,8) = HCF(40,32) = HCF(272,40) = HCF(312,272) = HCF(896,312) .


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

Step 1: Since 457 > 8, we apply the division lemma to 457 and 8, to get

457 = 8 x 57 + 1

Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 1 and 8, to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8 and 457 is 1

Notice that 1 = HCF(8,1) = HCF(457,8) .


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

Step 1: Since 188 > 1, we apply the division lemma to 188 and 1, to get

188 = 1 x 188 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 188 is 1

Notice that 1 = HCF(188,1) .

HCF using Euclid's Algorithm Calculation Examples

Frequently Asked Questions on HCF of 312, 896, 457, 188 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 312, 896, 457, 188?

Answer: HCF of 312, 896, 457, 188 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 312, 896, 457, 188 using Euclid's Algorithm?

Answer: For arbitrary numbers 312, 896, 457, 188 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.