**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 87, 64, 40 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 87, 64, 40 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 87, 64, 40 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 87, 64, 40 is **1**.

HCF(87, 64, 40) = 1

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

Highest common factor (HCF) of 87, 64, 40 is **1**.

**Step 1:** Since 87 > 64, we apply the division lemma to 87 and 64, to get

87 = 64 x 1 + 23

**Step 2:** Since the reminder 64 ≠ 0, we apply division lemma to 23 and 64, to get

64 = 23 x 2 + 18

**Step 3:** We consider the new divisor 23 and the new remainder 18, and apply the division lemma to get

23 = 18 x 1 + 5

We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get

18 = 5 x 3 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 87 and 64 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(23,18) = HCF(64,23) = HCF(87,64) .

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

**Step 1:** Since 40 > 1, we apply the division lemma to 40 and 1, to get

40 = 1 x 40 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 40 is 1

Notice that 1 = HCF(40,1) .

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 87, 64, 40?

Answer: HCF of 87, 64, 40 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 87, 64, 40 using Euclid's Algorithm?

Answer: For arbitrary numbers 87, 64, 40 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.