**Data: **

A = integers divisible by 3

B = integers divisible by 5

C = integers divisible by 7

Total integers = 500

**Formula:**

A ∪ B ∪ C = A + B + C – (A ꓵ B) – (A ꓵ C) – (B ꓵ C) + (A ꓵ B ꓵ C)

**Calculation: **

A = \(\frac{{500}}{3}\) , B = \(\frac{{500}}{5}\), C = \(\frac{{500}}{7}\), A ꓵ B = \(\frac{{500}}{{3 \times 5}}\)

A ꓵ C = \(\frac{{500}}{{3 \times 7}}\),

B ꓵ C = \(\frac{{500}}{{5 \times 7}}\) and A ꓵ B ꓵ C = \(\frac{{500}}{{3 \times 5 \times \;7}}\)

A ∪ B ∪ C = \(\frac{{500}}{3} + \frac{{500}}{5} + \frac{{500}}{7} - \frac{{500}}{{3 \times 5}} - \frac{{500}}{{3 \times 7}} - \frac{{500}}{{5 \times 7}} + \frac{{500}}{{3 \times 5 \times \;7}}\)

= 271

Number of integers divisible by 3 or 5 or 7 = 271