0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

State whether True or False.
j is divisible by 12 and 10, then j divisible by 24.
  1. True
  2. False

A
True
B
False
Solution
Verified by Toppr

The correct option is B False
If j is divisible by 12 and by 10, its prime factors include 2, 2, 3, and 5,
What is the minimum number of 2's necessary to create 12 or 10 ? You need two 2's to create 12. You could use one of those same 2's to create the 10. Therefore, there are only two 2's that are definitely in the prime factorization of j, because the 2 in the prime factorization of 10 may be redundant that is, it may be the same 2 as one of the 2's in the prime factorization of 12.
Factoring 24, you get 2 × 2 × 2 × 3. The prime box of j contains at least two 2's and could contain more. The number 24 requires three 2's. Therefore, you may or may not be able to create 24. Thus, 24 is not necessarily a factor of j.

Was this answer helpful?
0
Similar Questions
Q1
State whether True or False.
j is divisible by 12 and 10, then j divisible by 24.
View Solution
Q2
State whether true or false:
If a number is divisible by both 9 and 10, it must be divisible by 90.
View Solution
Q3

Question 81

In the following question, state whether the given statement is true (T) or false (F).

If a number is divisible by 2 and 3 both, then it is divisible by 12.

View Solution
Q4
State whether True or False:
13353 is divisible by 8

View Solution
Q5
State whether True or False
7 is a factor of n and 7 is a factor of p, then n + p divisible by 7
View Solution