CAT Factorials & highest power Questions

Factorials multiply consecutive positive integers. Highest-power questions count prime factors inside that product, and trailing zeros depend on complete factors of the representation's base.

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Key concepts

• Prime exponents in a factorial
• Highest power of a divisor
• Trailing zeros

CAT factorials & highest power practice questions

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Common mistakes

• Counting only multiples of a prime and missing additional copies in its powers.
• Using the exponent of one prime alone for a composite divisor.

Practical solving approaches

• Count contributions from successive powers of each required prime.
• For a composite divisor, factorise it and identify the limiting prime exponent.

Factorials & highest power FAQs

Why do decimal trailing zeros usually depend on factors of five?

Each zero requires a factor of ten, made from two and five. Factorials contain more twos than fives, so the number of fives is the limiting count.

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CAT Factorials & highest power Questions

Factorials multiply consecutive positive integers. Highest-power questions count prime factors inside that product, and trailing zeros depend on complete factors of the representation's base.

2 free practice questions

Key concepts

• Prime exponents in a factorial
• Highest power of a divisor
• Trailing zeros

CAT factorials & highest power practice questions

Question 1Type in the answerEASY

Question 1

Type in your answer in the input box provided below the question.

Answer the questions independently of each other.

What is the number of zeros at the end of 150!?

Your answer

Check answerView solution

Question 2Multiple choiceEASY

Question 2

Select the correct alternative from the given choices.

Answer the questions independently of each other.

Find the product of all the odd natural numbers less than 5000.

Choose an answer

A.

B.

C.

D.

Check answerView solution

Common mistakes

• Counting only multiples of a prime and missing additional copies in its powers.
• Using the exponent of one prime alone for a composite divisor.

Practical solving approaches

• Count contributions from successive powers of each required prime.
• For a composite divisor, factorise it and identify the limiting prime exponent.

Factorials & highest power FAQs

Why do decimal trailing zeros usually depend on factors of five?

Each zero requires a factor of ten, made from two and five. Factorials contain more twos than fives, so the number of fives is the limiting count.

More Number Systems practice

• Base systems →
• Factors, divisibility, HCF & LCM →
• Number properties & digits →
• Remainders & modular arithmetic →