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Excerpt from Beast Academy Practice 5B. (C) 2016 www.BeastAcademy.com
FACTORS & MULTIPLES
D iv isib ilit y
EXAMPLE
Which of the numbers below is divisible by 28?
2 • 5 ••••2 •••
The prime factorization of 28 is 22 •5QCPWODGTVJCVKUFKXKUKDNGD[OWUVJCXGCV
NGCUVVYQŏUCPFQPGKPKVURTKOGHCEVQTK\CVKQP
2 • 5 ••
5KPEGVJGTGKUPQKPVJGRTKOGHCEVQTK\CVKQPQHKVKUPQVFKXKUKDNGD[
••2 • 11:
5KPEGVJGRTKOGHCEVQTK\CVKQPQHJCUCVNGCUVVYQŏUCPFQPGKVKUFKXKUKDNGD[
••2 •
• 2 •• 2 • ••
• 2 ••• 11.
••:
5KPEGVJGTGKUQPN[QPGKPVJGRTKOGHCEVQTK\CVKQPQHKVKUPQVFKXKUKDNGD[
So, the only number above that is divisible by 28 is 12,936.
PRACTICE
Answer each question below.
17.
%KTENGGXGT[PWODGTDGNQYVJCVKUFKXKUKDNGD[
• 52•2 •2• • • • 5
18.
%KTENGGXGT[PWODGTDGNQYVJCVKUFKXKUKDNGD[
5 •• 5 • •2 •2 ••2 ••2 •2 • 11
19.
%KTENGGXGT[PWODGTDGNQYVJCVKUCHCEVQTQH2 • 5 ••
20.
%KTENGGXGT[PWODGTDGNQYVJCVKUCHCEVQTQH5 •2 • 19.
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)WKFG2CIGU
Beast Academy Practice 5B
Excerpt from Beast Academy Practice 5B. (C) 2016 www.BeastAcademy.com
FACTORS & MULTIPL
Divi si biES
li t y
EXAMPLE
The prime factorization of 11,625 is • 5 •
What is 11,625÷155?
The prime factorization of 155 is 5 •
We can use prime factorization to write 11,625 as the product of 155
and another integer:
• 5 •
• 5 • 5 • 5 •
••
• 5 • 5)
•
5KPEG• YGJCXGÒ 75 .
PRACTICE
Answer each question below.
21.
6JGRTKOGHCEVQTK\CVKQPQHKU • 52 •9JCVKUÒ!
21. ________
22.
6JGRTKOGHCEVQTK\CVKQPQHKU •2 •9JCVKUÒ!
22. ________
23.
6JGRTKOGHCEVQTK\CVKQPQHKU2 • • 5 •9JCVPWODGTECPDG
OWNVKRNKGFD[VQIGV!
23. ________
24.
+XCPFKXKFGUD[KVUNCTIGUVQFFHCEVQT9JCVKUVJGTGUWNV!
24. ________
25.
6JGRTKOGHCEVQTK\CVKQPQHKU5 • • 52. What is the smallest
KPVGIGTSWQVKGPV/[TVNGECPIGVKHUJGFKXKFGUD[CRQYGTQH!
25. ________
Beast Academy Practice 5B
)WKFG2CIGU
37
Excerpt from Beast Academy Practice 5B. (C) 2016 www.BeastAcademy.com
FACTORS & MULTIPLES
P e rfe ct Squa re s
EXAMPLE
Which of the following are perfect squares?
• 112 • 52 •2
A perfect square is the product of an integer and itself. So, we try to split the
prime factorizations above into two identical groups of prime factors.
9GECPFQVJKUHQTCPFHQT
•••
••
•
•
2.
28,900 5 • 2 • 5 • 5 ••
• 5 •• (2 • 5 •
•
2.
2 •
2 •
2
Review perfect
squares in
Chapter 5 of Beast
Academy 3B.
However, 2• 11
2 • 2 • 2 • 2 • 11 • 11 • 11
• 2 • 11) • (2 • 2 • 11) • 11.
There is no way to group the last 11 so that we have two identical
groups of factors.
So, only 2,401 and 28,900 are perfect squares.
PRACTICE
Answer each question below.
26.
Write the prime factorization of each perfect square below.
AAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAA
27.
Write each prime factorization below as a perfect square.
2 •
202
Ex: 2 • 52AAAA
112AAAA8AAAA •2 •2AAAA
28.
Circle every number below that is a perfect square.
5 •56 •22 • 112 •2 •2 • 19
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Beast Academy Practice 5B
Excerpt from Beast Academy Practice 5B. (C) 2016 www.BeastAcademy.com
FACTORS &Perf
MULTIPL
ect Sq u aES
res
PRACTICE
29.
Answer each question below.
Circle each number below that is a perfect square when x and y are different prime numbers.
x5 • y 5
x81
x2 • y y12
x•y
x • y10
30.
Grogg says that if a number is a perfect square, then its prime factorization includes only
even exponents. Lizzie says that if the prime factorization of a number includes only even
exponents, then the number is a perfect square. Who is correct: Grogg, Lizzie, or both?
Explain.
31.
Is 9 a perfect square? If so, write 9 as a perfect square. If not, explain why not.
32.
What is the smallest positive integer n for which 180n is a perfect
square?
32. ________
33.
6JGRTKOGHCEVQTK\CVKQPQHKU•2 •. What is the smallest
RQUKVKXGKPVGIGTVJCVECPDGOWNVKRNKGFD[VQOCMGCRGTHGEV
square?
33. ________
34.
9JCVKUVJGNCTIGUVRGTHGEVUSWCTGHCEVQTQH5 •• 5 •2?
34. ________
Beast Academy Practice 5B
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