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Explain why 3×5×7×11+11 is a composite number. |
| Answer» Answer:Composite numbers also known as composites in Mathematics are numbers that have more than 2 factors, not like prime numbers that have only one factor, i.e. 1 and the number itself.Composite numbers are all natural numbers that are not prime numbers since they can be divided by more than two numbers.6 is composite, for instance, since it is divisible by 1, 2, 3 and even 6.Now consider7 x 11 x 13 + 13We can also write this as⇒ (77 + 1) x 13⇒ 1014So the factors are⇒ 13 x 13 x 3 x 2It is a composite number. The given number has more than two factors.Now consider7 x 6 x 5 x 4 x 3 x 2 x 1 + 5We can also write it as⇒ 5(7 x 6 x 5 x 4 x 3 x 2 x 1 + 1)By calculation we get⇒ 1009 x 5It is a composite number. The given number has more than two factors.Hence proved. | |