HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 90, 120 i.e. 30 the largest integer that leaves a remainder zero for all numbers.

HCF of 90, 120 is 30 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 90, 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 90, 120 is **30**.

HCF(90, 120) = 30

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

Highest common factor (HCF) of 90, 120 is **30**.

**Step 1:** Since 120 > 90, we apply the division lemma to 120 and 90, to get

120 = 90 x 1 + 30

**Step 2:** Since the reminder 90 ≠ 0, we apply division lemma to 30 and 90, to get

90 = 30 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 90 and 120 is 30

Notice that 30 = HCF(90,30) = HCF(120,90) .

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 90, 120?

Answer: HCF of 90, 120 is 30 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 90, 120 using Euclid's Algorithm?

Answer: For arbitrary numbers 90, 120 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.