Answer:
18
<h2>What is HCF?</h2>
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).
<h2>How would we use this when finding the HCF of 54, 90, and 72?</h2>
<u>Step 1</u>: Since 90 > 54, we apply the division lemma to 90 and 54, to get
90 = 54 x 1 + 36
<u>Step 2</u>: Since the reminder 54 ≠ 0, we apply division lemma to 36 and 54, to get
54 = 36 x 1 + 18
<u>Step 3</u>: 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
<u>Step 1</u>: 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) .
<h2>What is the Euclid division algorithm?</h2>
Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
<h2>what is the HCF of 54, 90, 72?</h2>
HCF of 54, 90, 72 is 18 the largest number that divides all the numbers leaving a remainder zero.
<h2> How to find HCF of 54, 90, 72 using Euclid's Algorithm?</h2>
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.
