HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 45, 60, 120 i.e. 15 the largest integer that leaves a remainder zero for all numbers.

HCF of 45, 60, 120 is 15 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 45, 60, 120 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 45, 60, 120 is **15**.

HCF(45, 60, 120) = 15

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

Highest common factor (HCF) of 45, 60, 120 is **15**.

**Step 1:** Since 60 > 45, we apply the division lemma to 60 and 45, to get

60 = 45 x 1 + 15

**Step 2:** Since the reminder 45 ≠ 0, we apply division lemma to 15 and 45, to get

45 = 15 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 45 and 60 is 15

Notice that 15 = HCF(45,15) = HCF(60,45) .

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

**Step 1:** Since 120 > 15, we apply the division lemma to 120 and 15, to get

120 = 15 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 15 and 120 is 15

Notice that 15 = HCF(120,15) .

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 45, 60, 120?

Answer: HCF of 45, 60, 120 is 15 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 45, 60, 120 using Euclid's Algorithm?

Answer: For arbitrary numbers 45, 60, 120 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.