Factors

Factors are the numbers that multiply together to produce a specific number called the product. If multiplying two numbers gives a certain result, both of those starting numbers are factors of that final product.

Products and factors

When two numbers are multiplied, the answer obtained is called the product. The numbers used to produce that answer are its factors. For instance, four multiplied by two equals eight, which makes four and two factors of eight. Because eight multiplied by one also equals eight, the full set of factors for eight is one, two, four, and eight.

The jumping race rules

Factors can be found by imagining a track made of numbered boxes leading up to a pit at the target number.

• Each number enters the race and jumps forward by its own value.
• Number one moves forward one box at a time, while number two leaps two boxes at a time.
• Higher numbers jump three, four, or more boxes with each leap.
• Any number that lands directly in the pit at the end is a factor of that target number.
• Any number that leaps over the pit and misses it is not a factor.

Finding the factors of six

To find the factors of six, a pit is placed at box six on the running track. Number one lands on every box and falls into the pit. Number two and number three jump in steps of two and three, and both land exactly on six. Number four jumps from four to eight, completely missing six, so it is not a factor. Number six lands in the pit with a single jump, which means the factors of six are one, two, three, and six.

Finding the factors of five

To find the factors of five, the pit is placed at box five. Number one lands on box five because it moves one step at a time. Numbers two, three, and four jump along the track but fail to land in the pit at five. Number five jumps straight into the pit on its very first move. Therefore, the only numbers that land in the pit are one and five, making them the factors of five.