No, when there is a remainder, the divisor is not a factor of the dividend.
Understanding Factors and Division with Remainders
A factor of a number divides into that number evenly, leaving no remainder. Division is the process of splitting a number (the dividend) into equal groups determined by another number (the divisor). The result is the quotient, and if the dividend is not perfectly divisible by the divisor, there will be a remainder.
- Dividend: The number being divided.
- Divisor: The number by which the dividend is being divided.
- Quotient: The result of the division (how many times the divisor goes into the dividend).
- Remainder: The amount "left over" when the dividend cannot be divided evenly by the divisor.
The Relationship Between Factors and Remainders
The key relationship is:
- If the remainder is zero, then the divisor is a factor of the dividend.
- If the remainder is not zero, then the divisor is not a factor of the dividend.
Examples
-
Example 1: No Remainder (Divisor is a Factor)
- Dividend: 12
- Divisor: 3
- 12 ÷ 3 = 4 (Quotient) with a remainder of 0.
- Because the remainder is 0, 3 is a factor of 12.
-
Example 2: Remainder Exists (Divisor is Not a Factor)
- Dividend: 13
- Divisor: 3
- 13 ÷ 3 = 4 (Quotient) with a remainder of 1.
- Because the remainder is 1 (not zero), 3 is not a factor of 13.
Why Remainders Matter
The presence of a remainder indicates that the divisor doesn't divide the dividend into whole, equal groups. This means the divisor doesn't fit perfectly into the dividend, and therefore isn't a factor.
