Numbers and operations (factors, multiples, properties) — ISEE Upper practice questions

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Practice 118 Numbers and operations (factors, multiples, properties) questions in the app

What this topic is

Number sense matters more than lengthy computation in Numbers and operations (factors, multiples, properties), part of the Mathematics Achievement section.

Prime factorization is central: to count the factors of a number, add one to each exponent in its prime factorization and multiply, so two cubed times three has four times two, or eight, factors. Greatest common factor and least common multiple appear in word problems about grouping and repeating schedules.

Some questions ask which expression equals a given number, testing properties such as the distributive property. Estimation items round each factor before multiplying. Because choices are often close, a careful check is worthwhile.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

Which expression is equivalent to 48?

(8 \times 3) + 4 \times (7 - 1)

✓ Correct

8 \times (3 + 4) \times (7 - 1)

✗ Not this one

8 \times 3 \times 4 \times (7 - 1)

✗ Not this one

(8 \times 3 + 4) \times (7 - 1)

✗ Not this one

Show answer

Answer: A — $(8 \times 3) + 4 \times (7 - 1)$

(8 \times 3) + 4 \times 6 = 24 + 24 = 48

Question 2Easier

A positive integer $N$ has prime factorization $2^{4} \times 3^{2} \times 5$ . How many positive factors does $N$ have?

16✗ Not this one24✗ Not this one30✓ Correct48✗ Not this one

Show answer

Answer: C — 30

If $N = p^{a} q^{b} r^{c}$ , the number of positive factors is $(a + 1) (b + 1) (c + 1)$ . Here $(4 + 1) (2 + 1) (1 + 1) = 5 \cdot 3 \cdot 2 = 30$ . Using the exponents alone or omitting a factor produces the distractors.

Question 3Easier

What is the estimated product of $6.2 \times 4.7$ ? (Round each factor to the nearest whole number.)

24✗ Not this one29.14✗ Not this one30✓ Correct35✗ Not this one

Show answer

Answer: C — 30

Rounding gives $6.2 \approx 6$ and $4.7 \approx 5$ , so the estimated product is $6 \times 5 = 30$ .

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 118 Numbers and operations (factors, multiples, properties) questions in the app

Numbers and operations (factors, multiples, properties) — ISEE Upper practice questions

What this topic is

Sample questions

More ISEE Upper topics

Mathematics Achievement