Here is the solution for Class 10th Telangana SCERT Mathematics, Chapter number 1, Exercise 1.2 question number 4 which is Explain why 7 x 11 x 13 + 13 and 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 are composite numbers.
4) Explain why 7 x 11 x 13 + 13 and 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 are composite numbers
Solution: Definition of composite number
Composite numbers are whole numbers that can be divided by numbers other than itself, Ex: 4, 6, 8, 10 etc.
Given,
= 7 x 11 x 13 + 13.
= 13 [ 7 x 11 x 1 + 1 ].
= 13 [ 77 + 1 ].
= 13 x 78.
Since, the given numbers are in the form of 13x78, which indicate as a composite number.
Similarly,
= 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5.
= 5 [ 7 x 6 x 1 x 4 x 3 x 2 x 1 ].
= 5 [ 42 x 24 + 1 ].
= 5 [ 1008 + 1 ].
= 5 x 1009.
