**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 688, 997, 148 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 688, 997, 148 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 688, 997, 148 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 688, 997, 148 is **1**.

HCF(688, 997, 148) = 1

*Highest common factor* or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

Highest common factor (HCF) of 688, 997, 148 is **1**.

**Step 1:** Since 997 > 688, we apply the division lemma to 997 and 688, to get

997 = 688 x 1 + 309

**Step 2:** Since the reminder 688 ≠ 0, we apply division lemma to 309 and 688, to get

688 = 309 x 2 + 70

**Step 3:** We consider the new divisor 309 and the new remainder 70, and apply the division lemma to get

309 = 70 x 4 + 29

We consider the new divisor 70 and the new remainder 29,and apply the division lemma to get

70 = 29 x 2 + 12

We consider the new divisor 29 and the new remainder 12,and apply the division lemma to get

29 = 12 x 2 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 688 and 997 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(29,12) = HCF(70,29) = HCF(309,70) = HCF(688,309) = HCF(997,688) .

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

**Step 1:** Since 148 > 1, we apply the division lemma to 148 and 1, to get

148 = 1 x 148 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 148 is 1

Notice that 1 = HCF(148,1) .

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

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 688, 997, 148?

Answer: HCF of 688, 997, 148 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 688, 997, 148 using Euclid's Algorithm?

Answer: For arbitrary numbers 688, 997, 148 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.