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

On the ISEE Upper Mathematics Achievement section, Numbers and operations (factors, multiples, properties) covers primes, composites, factorizations, multiples, and properties of whole numbers and decimals. A student must rewrite a value as an equivalent expression, count positive factors from prime-factor form, and estimate a product by rounding each factor to the nearest whole number. Questions are multiple choice with numeric or expression options that look alike. Common traps include mixing factors with multiples, omitting a factor, adding exponents instead of using one more than each exponent, and rounding the wrong way before multiplying.

  • Section: Mathematics Achievement 47 questions on the paper
  • 117 practice questions in the app

Sample questions

Question 1

Which expression is equivalent to 48?

  1. A(8×3)+4×(7−1)(8 \times 3) + 4 \times (7 - 1)
  2. B8×(3+4)×(7−1)8 \times (3 + 4) \times (7 - 1)
  3. C8×3×4×(7−1)8 \times 3 \times 4 \times (7 - 1)
  4. D(8×3+4)×(7−1)(8 \times 3 + 4) \times (7 - 1)
Show answer

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

(8×3)+4×6=24+24=48(8\times3)+4\times6=24+24=48.

Question 2

A positive integer NN has prime factorization 24×32×52^{4}\times 3^{2}\times 5. How many positive factors does NN have?

  1. A16
  2. B24
  3. C30
  4. D48
Show answer

Answer: C — 30

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

Question 3

Estimate 6.2×4.76.2\times4.7 by rounding each factor to the nearest whole number. What is the estimated product?

  1. A24
  2. B29.14
  3. C30
  4. D35
Show answer

Answer: C — 30

Rounding gives 6.2≈66.2\approx6 and 4.7≈54.7\approx5, so the estimated product is 6×5=306\times5=30.

Practice 117 Numbers and operations (factors, multiples, properties) questions in the app

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