Highest Common Factor of 312, 379, 688 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, 379, 688 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 312, 379, 688 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, 379, 688 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, 379, 688 is 1.

HCF(312, 379, 688) = 1

HCF of 312, 379, 688 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, 379, 688 is 1.

Highest Common Factor of 312,379,688 using Euclid's algorithm

Highest Common Factor of 312,379,688 is 1

Step 1: Since 379 > 312, we apply the division lemma to 379 and 312, to get

379 = 312 x 1 + 67

Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 67 and 312, to get

312 = 67 x 4 + 44

Step 3: We consider the new divisor 67 and the new remainder 44, and apply the division lemma to get

67 = 44 x 1 + 23

We consider the new divisor 44 and the new remainder 23,and apply the division lemma to get

44 = 23 x 1 + 21

We consider the new divisor 23 and the new remainder 21,and apply the division lemma to get

23 = 21 x 1 + 2

We consider the new divisor 21 and the new remainder 2,and apply the division lemma to get

21 = 2 x 10 + 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 312 and 379 is 1

Notice that 1 = HCF(2,1) = HCF(21,2) = HCF(23,21) = HCF(44,23) = HCF(67,44) = HCF(312,67) = HCF(379,312) .

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

Step 1: Since 688 > 1, we apply the division lemma to 688 and 1, to get

688 = 1 x 688 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 688 is 1

Notice that 1 = HCF(688,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 312, 379, 688 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, 379, 688?

Answer: HCF of 312, 379, 688 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 312, 379, 688 using Euclid's Algorithm?

Answer: For arbitrary numbers 312, 379, 688 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.