Divisor

Definition

A divisor is a number that divides another number without leaving a remainder. It is a fundamental concept in mathematics, particularly in the operations of division and factorization, that is essential for understanding various mathematical topics.

5 Must Know Facts For Your Next Test

1. The divisor is the number that is used to divide another number, and it determines the number of equal parts the dividend is divided into.
2. In the context of dividing whole numbers, the divisor is the number that is used to divide the dividend, and the result is the quotient.
3. In the process of prime factorization, the divisors of a number are the prime factors that, when multiplied together, result in the original number.
4. When multiplying and dividing integers, the divisor determines the size and sign of the quotient.
5. In decimal operations, the divisor is the number that is used to divide the dividend, and it affects the placement of the decimal point in the quotient.

Review Questions

• Explain the role of the divisor in the division of whole numbers.
  • The divisor is the number that is used to divide the dividend in the operation of division. It determines how many equal parts the dividend is divided into. For example, if we are dividing 24 by 6, the divisor is 6, and the result is 4, as 24 is divided into 4 equal parts of 6 each.
• Describe the relationship between the divisor and the prime factorization of a number.
  • In the process of prime factorization, the divisors of a number are the prime factors that, when multiplied together, result in the original number. For instance, the prime factorization of 24 is 2 × 2 × 2 × 3, and the divisors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, which are all the possible combinations of these prime factors.
• Analyze the impact of the divisor on the result when multiplying and dividing integers.
  • $$\text{When multiplying and dividing integers, the divisor determines the size and sign of the quotient. If the divisor is a positive number, the quotient will have the same sign as the dividend. If the divisor is a negative number, the quotient will have the opposite sign of the dividend. The size of the divisor also affects the magnitude of the quotient, as a larger divisor will result in a smaller quotient, and a smaller divisor will result in a larger quotient.}$$

Related terms

Dividend: The number that is being divided by the divisor.

Quotient: The result of dividing the dividend by the divisor.

Factor: A number that divides another number evenly, without a remainder.