Question

What is the hcf of 54,90 and 72

Answer 1

Answer:

18

What is HCF?

What is the Highest common factor? The biggest integer that divides all numbers is HCF, while the lowest integer that divides all numbers is LCM (Lowest common multiple).

How would we use this when finding the HCF of 54, 90, and 72?

Step 1: Since 90 > 54, we apply the division lemma to 90 and 54, to get

90 = 54 x 1 + 36

Step 2: Since the reminder 54 ≠ 0, we apply division lemma to 36 and 54, to get

54 = 36 x 1 + 18

Step 3: We consider the new divisor 36 and the new remainder 18, and apply the division lemma 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 90 is 18

Notice that 18 = HCF(36,18) = HCF(54,36) = HCF(90,54) .

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

Step 1: Since 72 > 18, we apply the division lemma to 72 and 18, 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 18 and 72 is 18

Notice that 18 = HCF(72,18) .

What is the Euclid division algorithm?

Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

what is the HCF of 54, 90, 72?

HCF of 54, 90, 72 is 18 the largest number that divides all the numbers leaving a remainder zero.

How to find HCF of 54, 90, 72 using Euclid's Algorithm?

For arbitrary numbers 54, 90, 72 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.