If a three digit number ‘abc’ has 2 factors (where a, b, c are digits), how many factors does the 6-digit number ‘abcabc’ have?

a)
16

b)
24

c)
18

d)
30

Correct answer is option 'A'. Can you explain this answer?

Question

If a three digit number &lsquo;abc&rsquo; has 2 factors (where a, b, c are digits), how many factors does the 6-digit number &lsquo;abcabc&rsquo; have?a)16b)24c)18d)30Correct answer is option 'A'. Can you explain this answer?

Answer

The correct option is A

16

'abc' has 2 factors.

This means 'abc' is a prime number (Only a prime number can have exactly 2 factors).

Now, 'abcabc' = 'abc'×1001

'abcabc' = 'abc' × 7 × 11 × 13

Since 'abc' is prime we can write 'abcabc' as - p¹×7¹×11¹×13¹

No. of factors = (1+1) (1+1) (1+1) (1+1) = 16 factors.

Answer

If a three digit number is multiplied by its reverse, the result is always a palindrome.

For example, let's take the number 321.

The reverse of 321 is 123.

When we multiply 321 by 123, we get 39,483.

39,483 is a palindrome because it reads the same backward as forward.

Answer

A

Answer

A is the answer

Answer

Factors: Beauty of the number 1001. This number is not prime, is a product of three distinct primes and does wonderful things to three-digit numbers when multiplied to them.

To start with ‘abcabc’ = ‘abc’ * 1001 or abc * 7 * 11 * 13 (This is a critical idea to remember).

‘abc’ has only two factors. Or, ‘abc’ has to be prime. Only a prime number can have exactly two factors. (This is in fact the definition of a prime number)

So, ‘abcabc’ is a number like 101101 or 103103.

’abcabc’ can be broken as ‘abc’ * 7 * 11 * 13. Or, a p * 7 * 11 * 13 where p is a prime.

As we have already seen, any number of the form paqbrc will have (a + 1) (b + 1) (c + 1) factors, where p, q, r are prime.

So, p * 7 * 11 * 13 will have = (1 + 1) * (1 + 1) * (1 + 1) * (1 + 1) = 16 factors

The question is "How many factors does the 6-digit number ‘abcabc’ have?"

Hence the answer is 16 factors.
Choice A is the correct answer.

Answer

Answer is 16
6 digit number has 16 factor
(1+1)(1+1)(1+1)(1+1)
abc is prime number because only prime number has 2 factors

Answer

16

Answer

Factors: Beauty of the number 1001. This number is not prime, is a product of three distinct primes and does wonderful things to three-digit numbers when multiplied to them.

To start with ‘abcabc’ = ‘abc’ * 1001 or abc * 7 * 11 * 13 (This is a critical idea to remember).

‘abc’ has only two factors. Or, ‘abc’ has to be prime. Only a prime number can have exactly two factors. (This is in fact the definition of a prime number)

So, ‘abcabc’ is a number like 101101 or 103103.

’abcabc’ can be broken as ‘abc’ * 7 * 11 * 13. Or, a p * 7 * 11 * 13 where p is a prime.

As we have already seen, any number of the form paqbrc will have (a + 1) (b + 1) (c + 1) factors, where p, q, r are prime.

So, p * 7 * 11 * 13 will have = (1 + 1) * (1 + 1) * (1 + 1) * (1 + 1) = 16 factors

The question is "How many factors does the 6-digit number ‘abcabc’ have?"

Hence the answer is 16 factors.
Choice A is the correct answer.

Similar CAT Doubts

Find the number of 5 digit numbers formed using digits (0,1,2,4,6,8,9) when repeatition is allowed.

How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits? Correct answer is '6'. Can you explain this answer?

How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits? Correct answer is '6'. Can you explain this answer?

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