+0

# divisors

0
117
2

How many positive integers divide evenly into either 144 or 196 or 150?

Jul 24, 2022

#1
+2602
0

$$144 \Rightarrow 2^4 \times 3^2$$

$$196 \Rightarrow 2^2 \times 7^2$$

$$150 \Rightarrow 5^2 \times 2 \times 3$$

144 has $$5 \times 3 = 15$$ factors.

196 has $$3 \times 3 = 9$$ factors, but we need to subtract 3 (1, 2, and 4)

150 has $$2 \times 2 \times 3 = 12$$ factors, but we need to subtract 2 (1 and 2)

So, there are $$15 + 9 + 12 - 3 - 2 = \color{brown}\boxed{31}$$ numbers.

Jul 24, 2022
#2
0

(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 24, 25, 28, 30, 36, 48, 49, 50, 72, 75, 98, 144, 150, 196)==29 such divisors

Jul 24, 2022