CAT Quant · Chapter Test
Factors — 25-Question Test
A fresh, mixed-difficulty set drawn from the whole chapter — questions you haven't been asked before. Auto-graded with full solutions; your result is saved to your dashboard.
Building your 25-question test…
Formula Reference Sheet
This chapter
Core divisor formulas
| Prime factorisation | N = p^a × q^b × r^c (p, q, r distinct primes) |
|---|---|
| Number of factors | d(N) = (a+1)(b+1)(c+1) |
| Sum of factors | σ(N) = Π (p^(a+1) − 1)/(p − 1) |
| Product of factors | P(N) = N^(d/2), where d = d(N) |
| Number of odd factors | product of (exponent+1) for odd primes only |
Counting power-tools
| Ways = product of two factors | d/2 if N is not a perfect square; (d+1)/2 if it is |
|---|---|
| Number of even factors | d(N) − d(N with all 2s removed) |
| Factors that are perfect squares | Π (⌊exponent/2⌋ + 1) |
| Factors divisible by m | d(N) counted after dividing N by m (if m | N) |
| Number of co-prime pairs / sum of reciprocals | Σ(1/factor) = σ(N)/N |
CAT reference
🖩 Graphing Calculator