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PSAT Math : Factors / Multiples

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Example Questions

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Example Question #15 : How To Factor A Number

What is the smallest positive multiple of 12?

Possible Answers:

$\dpi{100} \small 24$

$\dpi{100} \small 2$

$\dpi{100} \small 0$

$\dpi{100} \small 12$

$\dpi{100} \small 6$

Correct answer:

$\dpi{100} \small 12$

Explanation:

Multiples of 12 are found by multiplying 12 by a whole number. Some examples include:

$\dpi{100} \small 12(-2)=-24$

$\dpi{100} \small 12(0)=0$

$\dpi{100} \small 12(1)=12$

Clearly, the smallest positive value obtainable is 12. Do not confuse the term multiple with the term factor!

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Example Question #11 : How To Factor A Number

How many prime factors of 210 are greater than 2?

Possible Answers:

four

three

five

two

one

Correct answer:

three

Explanation:

Begin by identifying the prime factors of 210. This can be done easily using a factoring tree (see image).

Vt_p2

The prime factors of 210 are 2, 3, 5 and 7. Of these factors, three of them are greater than 2.

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Example Question #11 : How To Factor A Number

How many integers between 50 and 100 are divisible by 9?

Possible Answers:

Correct answer:

Explanation:

The smallest multiple of 9 within the given range is $\inline \dpi{200} \tiny 54 = 9 \times 6$ .

The largest multiple of 9 within the given range is $\dpi{100} {99=9 \times 11}$ .

Counting the numbers from 6 to 11, inclusive, yields 6.

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Example Question #11 : How To Factor A Number

$\textup{If }a\textup{ is the greatest prime factor of 34 and }b\textup{ is the greatest}$

$\textup{prime factor of 20, what is the value of }a-b\textup{ ?}$

Possible Answers:

Correct answer:

Explanation:

Factor each number into prime roots:

$34=17\times2$

$20=5\times2\times2$

17-5=12

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PSAT Math : Factors / Multiples

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #15 : How To Factor A Number

Example Question #11 : How To Factor A Number

Example Question #11 : How To Factor A Number

Example Question #11 : How To Factor A Number

All PSAT Math Resources

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