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ISEE Upper Level Quantitative : How to factor a number

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

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All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #41 : How To Factor A Number

Which of the following is NOT a factor of $(32\cdot2)$ ?

Possible Answers:

Correct answer:

Explanation:

First, we must solve for $(32\cdot2)=64$

While 64 is divisible by 4, 8, and 16, it is not divisible by 7; therefore, 7 is not a factor of 64 and is thus the correct answer.

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Example Question #51 : Numbers And Operations

and are distinct odd primes. Which is the greater quantity?

(a) The number of factors of

(b) The number of factors of M + N

Possible Answers:

(b) is greater

(a) is greater

(a) and (b) are equal

It is impossible to tell which is greater from the information given

Correct answer:

It is impossible to tell which is greater from the information given

Explanation:

Since and are distinct primes, the prime factorization of is $M \cdot N$ ; therefore, the factors of are 1, , , and . There are four factors.

We show that M + N may or may not have more factors by example.

Case 1: M = 3, N = 5 .

Then M+N = 3+5 = 8 , which has four factors: 1, 2, 4, 8.

Case 2: M = 7, N = 5

Then M+N = 7+5 = 12 , which has six factors: 1, 2, 3, 4, 6, 12.

Therefore, we have at least one situation in which and M + N have the same number of factors, and at least one in which M + N has more. The given infomation is insufficient.

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Example Question #42 : How To Factor A Number

and are distinct odd primes. Which is the greater quantity?

(a) The number of factors of

(b) The number of factors of $N^{2}$

Possible Answers:

It is impossible to tell which is greater from the information given

(b) is greater

(a) and (b) are equal

(a) is greater

Correct answer:

(a) is greater

Explanation:

Since and are distinct primes, the prime factorization of is $M \cdot N$ ; therefore, the factors of are 1, , , and . There are four factors.

Since is a prime, the prime factorization of $N^{2}$ is $N \cdot N$ ; therefore, the factors of $N^{2}$ are 1, , and $N^{2}$ . There are three factors.

This makes (a) greater.

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All ISEE Upper Level Quantitative Resources

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ISEE Upper Level Quantitative : How to factor a number

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #41 : How To Factor A Number

Example Question #51 : Numbers And Operations

Example Question #42 : How To Factor A Number

All ISEE Upper Level Quantitative Resources

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