Question

1. Tom thought of a natural number, multiplied all its digits and after that he multiplied the result by the initial number. Is it possible to get 1716 as a result?
2. What is the largest prime factor of the factorial 49! ?

3. The GCD(a, b) = 18, LCM(a, b) = 108. If a=36, findb.

Answer 1

Answer:

1. No

2. 7

3. b=54

Step-by-step explanation:

1. We can answer this by assuming a number.

Let our number be 23

Multiplying its digits = 6

Multiplying the result with initial number = 6 * 23 = 138

So it is not possible to get 1716 as a result by thinking of a natural number and applying the operation mentioned in the question.

2. What is the largest prime factor of the factorial 49! ?

First of all we have to define prime factors:

Prime factors are the prime numbers that can be multiplied together to equal the original number.

The factors of 49 are: 1, 7, 49

7 is the largest prime factor of 49

3. The GCD(a, b) = 18, LCM(a, b) = 108. If a=36, findb.

We will use the relationship:

$GCD * LCM = a*b\\18*108=36b\\1944=36b\\b= \frac{1944}{36} \\b=54$

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