The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common ?

BTGModeratorVI wrote: ↑

Tue Feb 16, 2021 8:21 am

The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common ?

A. 10 and 20
B. 12 and 18
C. 24 and 32
D. 21 and 63
E. 22 and 88

Answer: C
Source: official guide

A. 10 and 20
10 = (2)(5)
20 = (2)(2)(5)
So, 10 and 20 both have 2 as a prime divisor, and they both have 5 has a prime divisor.
In other words, they have a PAIR a prime divisors in common
Eliminate A

B. 12 and 18
12 = (2)(2)(3)
18 = (2)(3)(3)
So, 12 and 18 both have 2 as a prime divisor, and they both have 3 has a prime divisor.
In other words, they have a PAIR a prime divisors in common
Eliminate B

C. 24 and 32
32 = (2)(2)(2)(2)(2)
So, 32 has only ONE distinct prime divisor
As such, it's impossible for 24 and 32 to have a PAIR a prime divisors in common

Answer: C

Cheers,
Brent

BTGModeratorVI wrote: ↑

Tue Feb 16, 2021 8:21 am

The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common ?

A. 10 and 20
B. 12 and 18
C. 24 and 32
D. 21 and 63
E. 22 and 88

Answer: C
Source: official guide

Solution:

Let’s consider each of the answer choices:

A) The GCF of 10 and 20 is 10, which is 2 times 5. So 10 and 20 do have a pair of distinct prime divisors in common.

B) The GCF of 12 and 18 is 6, which is 2 times 3. So 12 and 18 do have a pair of distinct prime divisors in common.

C) The GCF of 24 and 32 is 8, which is 2^3. So 24 and 32 do NOT have a pair of distinct prime divisors in common.

Answer: C