Divisibility is a fundamental concept in mathematics that helps us determine whether a number is evenly divisible by another number without leaving a remainder. In this article, we will delve into the realm of divisibility and explore the question, “What is 90 divisible by?” We will unravel the mathematical properties of 90 and present a comprehensive overview of all the numbers that 90 can be evenly divided by. So, buckle up and get ready to embark on a numerical adventure as we unravel the divisibility of 90.

To begin our exploration, let’s first establish the definition of divisibility. When a number, known as the dividend, is divided by another number, known as the divisor, it results in a quotient and a remainder. If the remainder is zero, we say that the dividend is divisible by the divisor. In other words, divisibility implies that the dividend can be expressed as a whole number multiple of the divisor.

Armed with this understanding, let’s turn our attention to the number 90. To determine what 90 is divisible by, we need to identify all the numbers that, when multiplied by a whole number, result in 90. This process involves systematic trial and error, starting with the smallest possible divisor and gradually moving upwards.

## Factors of 90

### Divisibility by 1 and 90

The most trivial divisors of any number are 1 and the number itself. In the case of 90, both 1 and 90 are divisors, as 90 divided by 1 is 90, and 90 divided by 90 is 1. These two divisors represent the lower and upper bounds of the range of divisors.

### Divisibility by 2

Moving on to the next possible divisor, we have 2. When we divide 90 by 2, we get 45. Since 45 is a whole number, 2 is a divisor of 90. This tells us that 90 is an even number, as it is divisible by 2.

### Divisibility by 3

Continuing our journey, we encounter the number 3. Upon dividing 90 by 3, we obtain 30. Once again, 30 is a whole number, confirming that 3 is another divisor of 90. This implies that 90 is not only divisible by 2 but also by 3.

### Divisibility by 5

Next in line is the number 5. When we attempt to divide 90 by 5, we get 18. As 18 is a whole number, 5 is also a divisor of 90. This tells us that 90 is divisible by 5, further expanding the list of its divisors.

### Divisibility by 6 and 15

Since 90 is divisible by both 2 and 3, it follows that it is also divisible by their product, 6. Similarly, as 90 is divisible by both 3 and 5, it is also divisible by their product, 15. Therefore, 6 and 15 are also divisors of 90.

### Divisibility by 9 and 10

Continuing our exploration, we encounter the number 9. Dividing 90 by 9 gives us 10. As 10 is a whole number, 9 is a divisor of 90. Additionally, as 90 is divisible by both 2 and 5, it is divisible by their product, 10.

### Divisibility by 18 and 45

Since 90 is divisible by both 2 and 9, it is divisible by their product, 18. Similarly, as 90 is divisible by both 3 and 15, it is divisible by their product, 45. Therefore, 18 and 45 are also divisors of 90.

### Divisibility by 30

Finally, as 90 is divisible by both 3 and 10, it is divisible by their product, 30. This makes 30 the largest proper divisor of 90.

## Conclusion

In conclusion, after a thorough investigation into the divisibility of 90, we have unveiled the complete list of its divisors: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90. This comprehensive understanding of the factors of 90 provides a solid foundation for further mathematical explorations and applications.

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