# Highest Common Factor of 72, 90, 120 using Euclid's algorithm

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 72, 90, 120 i.e. 6 the largest integer that leaves a remainder zero for all numbers.

HCF of 72, 90, 120 is 6 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 72, 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 72, 90, 120 is 6.

HCF(72, 90, 120) = 6

## HCF of 72, 90, 120 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 72, 90, 120 is 6.

### Highest Common Factor of 72,90,120 using Euclid's algorithm

Step 1: Since 90 > 72, we apply the division lemma to 90 and 72, to get

90 = 72 x 1 + 18

Step 2: Since the reminder 72 ≠ 0, we apply division lemma to 18 and 72, to get

72 = 18 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 72 and 90 is 18

Notice that 18 = HCF(72,18) = HCF(90,72) .

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

Step 1: Since 120 > 18, we apply the division lemma to 120 and 18, to get

120 = 18 x 6 + 12

Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 12 and 18, to get

18 = 12 x 1 + 6

Step 3: We consider the new divisor 12 and the new remainder 6, and apply the division lemma to get

12 = 6 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 18 and 120 is 6

Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(120,18) .

### HCF using Euclid's Algorithm Calculation Examples

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### Frequently Asked Questions on HCF of 72, 90, 120 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 72, 90, 120?

Answer: HCF of 72, 90, 120 is 6 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 72, 90, 120 using Euclid's Algorithm?

Answer: For arbitrary numbers 72, 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. 