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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

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Example Questions

Example Question #1 : Other Factors / Multiples

Which of these numbers is relatively prime with 18?

Possible Answers:

$\displaystyle 35$

$\displaystyle 33$

$\displaystyle 32$

$\displaystyle 34$

$\displaystyle 39$

Correct answer:

$\displaystyle 35$

Explanation:

For two numbers to be relatively prime, they cannot have any factor in common except for 1. The factors of 18 are 1, 2, 3, 6, 9, and 18.

We can eliminate 32 and 34, since each shares with 18 a factor of 2; we can also eliminate 33 and 39, since each shares with 18 a factor of 3. The factors of 35 are 1, 5, 7, and 35; as can be seen by comparing factors, 18 and 35 only have 1 as a factor, making 35 the correct choice.

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Example Question #11 : Factors / Multiples

Which of the following is the prime factorization of 333?

Possible Answers:

333 cannot be factorized further

$3 \times 3\times3\times13$ $\displaystyle 3 \times 3\times3\times13$

$3 \times 11 \times 11$ $\displaystyle 3 \times 11 \times 11$

$3 \times 3 \times 37$ $\displaystyle 3 \times 3 \times 37$

$3 \times 111$ $\displaystyle 3 \times 111$

Correct answer:

$3 \times 3 \times 37$ $\displaystyle 3 \times 3 \times 37$

Explanation:

To find the prime factorization, break the number down as a product of factors, then keep doing this until all of the factors are prime.

$333 = 3 \times 111 = 3 \times3 \times 37$ $\displaystyle 333 = 3 \times 111 = 3 \times3 \times 37$

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Example Question #12 : Factors / Multiples

Give the prime factorization of 91.

Possible Answers:

$91 = 7\times 13$ $\displaystyle 91 = 7\times 13$

$91 = 3 \times 3 \times 17$ $\displaystyle 91 = 3 \times 3 \times 17$

91 is a prime number.

$91 = 7 \times 17$ $\displaystyle 91 = 7 \times 17$

$91 = 3 \times 3 \times 13$ $\displaystyle 91 = 3 \times 3 \times 13$

Correct answer:

$91 = 7\times 13$ $\displaystyle 91 = 7\times 13$

Explanation:

$91 = 7 \times 13$ $\displaystyle 91 = 7 \times 13$

Both are prime factors so this is the prime factorization.

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Example Question #13 : Factors / Multiples

How many factors does 40 have?

Possible Answers:

$\displaystyle 6$

$\displaystyle 7$

$\displaystyle 9$

$\displaystyle 10$

$\displaystyle 8$

Correct answer:

$\displaystyle 8$

Explanation:

40 has as its factors 1, 2, 4, 5, 8, 10, 20, and 40 - a total of eight factors.

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Example Question #14 : Factors / Multiples

What is the sum of all of the factors of 27?

Possible Answers:

$\displaystyle 39$

$\displaystyle 36$

$\displaystyle 13$

$\displaystyle 12$

$\displaystyle 40$

Correct answer:

$\displaystyle 40$

Explanation:

27 has four factors: $\displaystyle 1, 3, 9, 27.$

Their sum is $\displaystyle 1 + 3 + 9 + 27 = 40$ .

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Example Question #15 : Factors / Multiples

Add all of the factors of 30.

Possible Answers:

$\displaystyle 41$

$\displaystyle 72$

$\displaystyle 71$

$\displaystyle 55$

$\displaystyle 42$

Correct answer:

$\displaystyle 72$

Explanation:

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. Their sum is

$\displaystyle 1+2+3+5+ 6+10+15 + 30 = 72$ .

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Example Question #7 : Other Factors / Multiples

Which is the greater quantity?

(a) The number of factors of 169

(b) The number of factors of 121

Possible Answers:

(a) is greater

(b) is greater

It is impossible to tell from the information given

(a) and (b) are equal

Correct answer:

(a) and (b) are equal

Explanation:

Each number has only three factors. 121 has 1, 11, and 121 as factors; 169 has 1, 13, and 169 as factors. The answer is that the quantities are equal.

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Example Question #8 : Other Factors / Multiples

Which is the greater quantity?

(a) The number of factors of 15

(b) The number of factors of 17

Possible Answers:

(b) is greater.

(a) and (b) are equal.

(a) is greater.

It is impossible to tell from the information given.

Correct answer:

(a) is greater.

Explanation:

(a) 15 has four factors, 1, 3, 5, and 15.

(b) 17, as a prime, has two factors, 1 and 17.

Therefore, (a) is greater.

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Example Question #9 : Other Factors / Multiples

Which is the greater quantity?

(a) The product of the integers between $\displaystyle -1,000,000$ and $\displaystyle 1,000,000$ inclusive

(b) The sum of the integers between $\displaystyle -1,000,000$ and $\displaystyle 1,000,000$ inclusive

Possible Answers:

(b) is greater.

It is impossible to tell from the information given.

(a) and (b) are equal.

(a) is greater.

Correct answer:

(a) and (b) are equal.

Explanation:

The quanitites are equal, as both can be demonstrated to be equal to .

(a) One of the integers in the given range is , so one of the factors will be , making the product .

(b) The sum of the numbers will be:

$\displaystyle 0 + (-1 + 1) + (-2 + 2) + (-3 + 3) + ... + (-1,000,000+ 1,000,000)$

$\displaystyle 0 + 0 + 0+...+0 = 0$

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Example Question #16 : Factors / Multiples

Which is the greater quantity?

(a) The sum of the factors of $\displaystyle 18$

(b) The sum of the factors of $\displaystyle 20$

Possible Answers:

It is impossible to tell from the information given.

(b) is greater.

(a) is greater.

(a) and (b) are equal.

Correct answer:

(b) is greater.

Explanation:

(a) The factors of $\displaystyle 18$ are $\displaystyle 1, 2, 3, 6, 9, 18.$ Their sum is

$\displaystyle 1+ 2+3+ 6+ 9+18 = 39$ .

(b) The factors of $\displaystyle 20$ are $\displaystyle 1, 2, 4, 5, 10, 20.$ Their sum is

$\displaystyle 1+ 2+4+5+10+20 = 42$ .

(b) is greater.

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All ISEE Upper Level Quantitative Resources

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

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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 #1 : Other Factors / Multiples

Example Question #11 : Factors / Multiples

Example Question #12 : Factors / Multiples

Example Question #13 : Factors / Multiples

Example Question #14 : Factors / Multiples

Example Question #15 : Factors / Multiples

Example Question #7 : Other Factors / Multiples

Example Question #8 : Other Factors / Multiples

Example Question #9 : Other Factors / Multiples

Example Question #16 : Factors / Multiples

All ISEE Upper Level Quantitative Resources

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