# Highest Common Factor of 54, 36, 90, 510 using Euclid's algorithm

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 54, 36, 90, 510 i.e. 6 the largest integer that leaves a remainder zero for all numbers.

HCF of 54, 36, 90, 510 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 54, 36, 90, 510 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 54, 36, 90, 510 is 6.

HCF(54, 36, 90, 510) = 6

## HCF of 54, 36, 90, 510 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 54, 36, 90, 510 is 6.

### Highest Common Factor of 54,36,90,510 using Euclid's algorithm

Step 1: Since 54 > 36, we apply the division lemma to 54 and 36, to get

54 = 36 x 1 + 18

Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 18 and 36, to get

36 = 18 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 54 and 36 is 18

Notice that 18 = HCF(36,18) = HCF(54,36) .

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

Step 1: Since 90 > 18, we apply the division lemma to 90 and 18, to get

90 = 18 x 5 + 0

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

Notice that 18 = HCF(90,18) .

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

Step 1: Since 510 > 18, we apply the division lemma to 510 and 18, to get

510 = 18 x 28 + 6

Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 6 and 18, to get

18 = 6 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 18 and 510 is 6

Notice that 6 = HCF(18,6) = HCF(510,18) .

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### Frequently Asked Questions on HCF of 54, 36, 90, 510 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 54, 36, 90, 510?

Answer: HCF of 54, 36, 90, 510 is 6 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 54, 36, 90, 510 using Euclid's Algorithm?

Answer: For arbitrary numbers 54, 36, 90, 510 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step. 