Manhattan Review Factors And Multiples

Factors and Multiples Integers are numbers that we can write in decimal notation without a decimal point. Every number between two consecutive integers is a non-integer. How many of the following are integers? -2

7

0

16/8

7/2

3.5

3

We say that 1, 2, 4, 5, 10 and 20 are factors of 20, and 20 is a multiple of 1, 2, 4, 5, 10 and 20. 3 is not a factor or divisor of 32 because 32/3 is not 45 is a multiple of 3 because 45 is equal to 3 multiplied by Is 0 a multiple of positive integer k ? Even numbers are integers that are divisible by If the product of two integers is even, then ________must be even. If the product of two integers is odd (not even), then ________ odd. If the sum of two integers is odd, the difference between the two integers is If k is an integer, 2k+1 is

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Prime numbers are positive integers with exactly two factors. The smallest prime number is All prime numbers greater than 2 are 96= 25 × 3 has two prime factors, but a total of ____ factors. Which number has more positive factors, 153 or 165 ? If 𝑛 is the product of 4 different prime numbers, how many factors does 𝑛 have that are between 1 and n? 8

10

12

14

16

If x  220 and y  105 , the smallest positive multiple of both x and y is the greatest divisor of both x and y is If positive integer x is a multiple of 4 and of 14, how many positive integers must be divisors of x? 3

4

5

6

8

308,000 = 3.08 × 105 = 308 × 103 has 3 trailing zeros. 2 If 𝑎 = 25 ×32 × 5 × 11 and 𝑏 = 4 × 25 × 13, how many trailing zeros does 𝑎𝑏 have? 4

5

6

8

31

10

When 76 is divided by 7, the quotient 𝑞 is the largest integer less than or equal to 76/7.Therefore, 𝑞 = The remainder when 76 is divided by 7 is 76 − 7𝑞 = When 76 is divided by 7, the quotient is 10 and the remainder is 6. We can write 76=10(7)+6 or 76/7= 10 +6/7=

10

6 7

When x is divided by 4, the remainder is 3. We can write x = If 𝑛 is an odd integer, 𝑛3 − 𝑛 must be a multiple of all of the following integers except 2

3

8

16

24

A perfect square is a number whose square root is also an integer. Circle the perfect squares. 121

0

399

64

24 53 205

If 𝑘 and 𝑚 are positive integers and 180𝑘 = 𝑚3 . What is the value of 𝑘 ? (1) 𝑘 < 200 (2) 𝑚 < 200

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If M is the set of distinct prime factors of positive integer m and N is the set of distinct prime factors of positive integer n, is M = N ? (1) m is not a factor of n, nor is n a factor of m. (2) m + n is a prime number greater than 2.

How many 4-digit positive integers are multiples of each integer from 1 to 10? 0

1

2

3

4

If s and t are integers so that 4s + t is odd and 3s + 5t is even, which of the following must be a multiple of 8? st( s +1 )2

s2t2

s3

st ( s – 1)( t + 1 )

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( t2 – 1 )( s + 1 )

Orange (GMAT Review 11th Edition) PS (Problem Solving) 2,5,21,33,37,56,71,88,108,114,148,159,161,184,187,198, 207,209,213,234,236,241,242,249 DS (Data Sufficiency) 14,17,22,25,28,45,61,65,101,103,107,118,125,132,134,146 147,148,149,153 Green (GMAT Quantitative Review) PS (Problem Solving) 9,29,60,98,102,103,109,125,144,150 163,164,169,172 DS (Data Sufficiency) 3,7,13,16,30,33,39,45,63,75,83,86 86,88,98,100,106,108,110,112,113,116

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