Question 25

It is a surprising fact that $$1\times2\times3\times4\times5\times6=8\times9\times10$$. It is more surprising that $$8\times9\times10\times11\times12\times13\times14$$ can be written as a product of consecutive positive integers. The smallest number in the product is $$\underline{\qquad}$$.

Correct Answer: 63

Solution

Factorising or multiplying shows $$8\mathbin{\times}9\mathbin{\times}10\mathbin{\times}11\mathbin{\times}12\mathbin{\times}13\mathbin{\times}14=17297280$$. Also, $$63\mathbin{\times}64\mathbin{\times}65\mathbin{\times}66=17297280$$. Thus the alternate consecutive product begins with $$63$$.

Get AI Help

Other Cracku’s Useful Resources:

JEE Questions JEE Question Bank JEE Mains Previous Papers JEE Advanced Previous Papers JEE Study Material PDF JEE Mains Mock Test JEE Advanced Mock Test JEE Daily Target

Free JEE Questions

JEE Physics Questions JEE Maths Questions JEE Chemistry Questions

It is a surprising fact that $$1\times2\times3\times4\times5\times6=8\times9\times10$$. It is more surprising that $$8\times9\times10\times11\times12\times13\times14$$ can be written as a product of consecutive positive integers. The smallest number in the product is $$\underline{\qquad}$$.

Solution

Get AI Help

Other Cracku’s Useful Resources:

Free JEE Questions

50,000+ JEE Students Trusted Our Score Calculator

Download resources