Download Altamont Pre-test - Weatherly Math Maniacs

Prime Numbers, Factors & Multiples
Practice
1. What is the smallest prime number? 2
2. How many prime numbers have value less than 100?
25
3. What is the largest prime number less than 500? 499
4. Find the largest prime number less than 100. 97
5. What is the sum of all primes less than 50? 328
6. The product of 3 different primes is always divisible by exactly 3_ different
non-prime numbers greater than 1.
7. Write 12 as a product of prime numbers. 2x2x3
8. Write 20 as a product of prime numbers. 2x2x5
9. List all the primes that 12 and 20 share.
numbers you just listed in #8. 4
2x2 or 22 Now multiply the
The result is called the greatest common factor, or GCF, of 12 and 20.
10.
Find the GCF of 28 and 36. 4
Additional question: What is the GCF of 24 and 36?
2x2x2x3 and 2x2x3x3  2x2x3 = 12
Page 1 of 3
What is a factor?
11.
List all pairs of factors of 12.
1 & 12,
2 & 6,
3&4
12.
List all pairs of factors of 20. 1 & 20, 2 & 10, 4 & 5
13.
Will there always three pairs of factors? no
14.
Are the factors always prime numbers? no
More Practice
15. 50 x 50 = 25 x 25 x 4
16.
and 80 x 80 x 80 = 20 x 20 x 20 x 4x4x4 (or 64)
27 ÷ 3 = 3 x 3
17.
18.
Two million equals:
c) 2000 x 1000
3 x 6 x 18 = 27 x ____ Solution: 3 x 2x3 x 3x3x2 = 3x3x3 x 2x2x3 (or 12)
19.
(32 x 4) + (32 x 5) + (32 x 6)
20.
How many positive two-digit numbers less than 40 have an odd number of
divisors? Answer: 3 Think about this: all divisors (factors) come in
pairs so unless there is a repeated divisor (like 4x4) there will be an even
number of divisors. So the perfect squares (16, 25, & 36) will have an
odd number of divisors.
21.
What is the sum of the numbers less than 35 that have exactly 8
factors? 24 + 30 = 54
22.
How many positive integer divisors does 144 have? 15: 1, 2, 3, 4, 6, 8,
9, 12, 16, 18, 24, 36, 48, 72, 144
23.
The greatest common divisor of 60, 160, and 260 is c) 20 (think of 6, 16,
and 26)
Short way: 32 x (4+5+6) = 32x15 = 480
24. Every even number has at least one even prime factor. (What is the only
even prime?)
25.
If I multiply two integers and their product is 36, their sum CANNOT be
a) 16 Consider factors pairs of 36: 1x36, 2x18, 3x12, 4x9, 6x6
Page 2 of 3
Multiples
Multiples of 2 are called even numbers.
Integers that are NOT divisible by 2 are called odd numbers. (Integers are
whole numbers and their opposites.
What do you get if you multiply two even numbers? Even
What is the product of an even and an odd? even
If you multiply an odd and an odd, you get an odd number.
Now, think of the same questions for the sum of two numbers:
even + even = even
even + odd = odd
and odd + odd = even
1. The product of 2009 and any even number is always even.
2. How many three-digit even numbers are greater than 827? 36
3. (33 + 44 + 55 + 66) ÷ 11 = 3+4+5+6 = 18
4. What is the largest multiple of 6 less than 1000? 996 (must be even and
divisible by 3)
5. What is the least common multiple of 6 and 9? 36
6. What is the LCM of 12 and 15? 60
7. Find the LCM of 10 and 16. 90
8.
9.
The smallest whole number divisible by both (same as asking for GCF of) 24
and 36 is 144
In the division (121,121,121,003) ÷ 11, what is the remainder?
b) 3
10. How many two-digit whole numbers are multiples of both 8 and 12?
4: 24, 48, 72, & 96
11. What is the product of the least common multiple and the greatest common
factor of 21 and 34?
LCM = 2 x 3 x 7 x 17= 714 

 so the product is 714 x 1 = 714
GCF = 1

Page 3 of 3