Playing with Numbers Test - 2

Factors of 64 = 1 × 64, 2 × 32,4 × 16, 8 × 8
= 1, 2, 4, 8, 16, 32, 64
= 7 factors

Factors of 80 = 1 × 80, 2 × 40, 4 × 20, 5 × 16, 8 × 10
= 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
= 10 factors

Factors of 84 = 1 × 84, 2 × 42, 3 × 28, 4 × 21, 6 × 14, 7 × 12
= 1,2,3,4,6,7,12,14,21,28,42,84
= 12 factors

Factors of 96 = 1 × 96, 2 × 48, 3 × 32, 4 × 24, 6 × 16, 8 × 12,
= 12 factors

2 and 3 are the prime factors of 6, so a number divisible by both of them will also be divisible be 6.

3 and 4 are the factors of 12, which is a multiple of 6. If a number is divisible by a multiple of 6, it will also be divisible by 6.

12 itself is a multiple of 6, so every number in the times table of 12 is also in the times table of 6. Therefore, if a number is divisible by 12, it will also be divisible by 6.

Any number that has more than two factors is called a composite number.
For example, 4 is a composite number because it has three factors 1, 2 and 4.

A number is divisible by 4 if the number formed by the last two digits of the number is divisible by 4.

Number formed by the last two digits of 457N8 = N8

For N8 to be a multiple of 4, the least possible number that can be formed is 08, which is a multiple of 4.

The least number which is divisible by 24, 28, 32 and 48 is the LCM of 24, 28, 32 and 48.

24 = 2 × 2 × 2 × 3
28 = 2 × 2 × 7
32 = 2 × 2 × 2 × 2 × 2
48 = 2 × 2 × 2 × 2 × 3

LCM = 2 × 2 × 2 × 2 × 3 × 2 × 7 = 672

Now, the required number is 7 less than the LCM.
I.e. 672 - 7 = 665

Smallest five-digit number = 10,000; which is exactly divisible by 50 because any number that ends with two or more zeros is divisible by 50.
Smallest six-digit number = 1,00,000; which is exactly divisible by 50 because any number that ends with two or more zeros is divisible by 50.

Product of the numbers = 32 × 1344 = 43008
One of the numbers is 96.

Let the other number be X.
So, 96 × X = 43008

X = 43008 ÷ 96
X = 448