It’s not new to say that 30 = 5×6. However, the factor set 5×6 is interesting, in a way.<\/p>\n
In math, n and n+1 (for instance, 5 and 6) are always relatively prime; that is, the only number that goes into both will be 1. Therefore, the only way a number has both factors n and n+1 is if both multiply together to make it (perhaps along with other numbers, depending on its size).<\/p>\n
\nAnother example is 84, which is 42×2 or 6x7x2. Once again, 6 and 7 both go into 84, and you need multiply them both together to make it. You can write 6 as 2×3, but it’s still there: (2×3)x7x2 = 84.<\/p>\n
\nNote that this isn’t necessarily true of other patterns. For instance, n and n+2 can both go into a number, but not both be part of its factorization. 4 and 6 both go into 12, for instance, but 4×6=24 rather than 12.\n<\/p>\n
\nTravers, Kenneth J. et al. Using Advanced Algebra.<\/em> Toronto: Doubleday Canada Limited, 1977.<\/p>\nJack of Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.\n","protected":false},"excerpt":{"rendered":" Tutoring math, number exploration is interesting. The tutor mentions 30 as an example of consecutive factors. It’s not new to say that 30 = 5×6. However, the factor set 5×6 is interesting, in a way. In math, n and n+1 …<\/p>\n