Study your flashcards anywhere!

Download the official Cram app for free >

  • Shuffle
    Toggle On
    Toggle Off
  • Alphabetize
    Toggle On
    Toggle Off
  • Front First
    Toggle On
    Toggle Off
  • Both Sides
    Toggle On
    Toggle Off
  • Read
    Toggle On
    Toggle Off
Reading...
Front

How to study your flashcards.

Right/Left arrow keys: Navigate between flashcards.right arrow keyleft arrow key

Up/Down arrow keys: Flip the card between the front and back.down keyup key

H key: Show hint (3rd side).h key

A key: Read text to speech.a key

image

Play button

image

Play button

image

Progress

1/57

Click to flip

57 Cards in this Set

  • Front
  • Back
When is an integer divisible by 2?
When the integer is EVEN.
When is an integer divisible by 3?
If the sum of the integer is divisible by 3.
36 is divisible by 3 because the sum 9 is divibile by 3.
When is an integer divisible by 4?
If the integer is divisible by 2 twice.
28 is divisible by 4 because it divisible by 2 once (=14) and again (=7)

Alternatively when the last 2 digits of the number are divisible by 4. For example 216 is divisible by 4 because 16 is divisible by 4.
When is an integer divisible by 5?
If the integer ends in 0 or 5 it is divisible by 5.
When is an integer divisible by 6?
If the integer is divisible by BOTH 2 and 3.
48 is divisible by 6 since it is divisible by 2 (48 is even) and by 3 (8+4=12).
When is an integer divisible by 8?
If the integer is divisible by 2 THREE times.
32/8=16/2=8/2=4

Or alternatively when the last 3 digits of that number is divisible by 8.

For example 2,889,888 is divisible by 8 because 888 is divisible by 8
When is an integer divisible by 9?
If the sum of the integer's DIGITS is divisible by 9.
4185 is divisible by 9 since the sum of its digits is 18, which is divisible by 9.
When is an integer divisible by 10?
If the integers ends in 0.
True or false are the sum and diffrence of an integer also divisible by that integer?
True.
8 is a factor of 64, and 8 is also a factor of 40. Another way to think about it is 64 is divisible by 8 and 40 is divisible by 8. The sum of 64 and 40 (64+40=104) is also divisible by 8 and the difference (64-40=24) is divisible by 8.
True or false you don't include 1 when counting the number of factors of a number?
False. 1 is a non-prime factor of all integers. You must include 1 when counting the factors of any number.
What is the definition of GCF?
Greatest Common Factor is defined as the largest integer by which two integers can be divided.
What is the definition of LCF?
Least Common Factor is the defined as the smallest number by which two integers can be multiplied.
How do you find the GCF using the prime box?
1. List the two primes boxes with their respective prime numbers.
2. Find the common primes numbers between the prime boxes.
3. Using the lowest power of the common prime number and multiply to find GCF.

For example:

What is GCF of 30 and 24?
1. List their prime boxes.

30 prime box is 2, 3, 5
24 prime box is 2, 2, 2, 3

2. List common primes between boxes. (i.e 2 and 3)

3. List the lowest power of these numbers and multiply them together. (i.e 2^1*3^1=6)
How do you find the LCF using the prime box?
1. List the two primes boxes with their resptive prime numbers.
2. List all prime factors between both prime boxes.
3. Multiple the primes using the highest power.

For examples.

1. List their prime boxes.

30 prime box is 2, 3, 5
24 prime box is 2, 2, 2, 3

2. List all primes between boxes. (i.e 2, 3 and 5)

3. List the highest power of these numbers and multiply them together. (i.e 2^3*3^1*5^1=120)
EVEN+EVEN
EVEN
EVEN+ODD
ODD
ODD+EVEN
ODD
ODD+ODD
EVEN
EVEN-EVEN
EVEN
EVEN-ODD
ODD
ODD-EVEN
ODD
ODD-ODD
EVEN
EVEN*EVEN
EVEN
EVEN*ODD
EVEN
ODD*EVEN
EVEN
ODD*ODD
ODD
True or false when you divide and even number with an odd number you get an even number?
False. It can't be determined. When you divided two integers the result may not yield an integer result.
True or false the sum of two primes is even if both of those primes are > 2?
True. 2 is the only even prime and all other primes are odd. Thus we have odd+odd=even. (i.e 3+5=8)
True or false the sum of two primes cannot be odd?
False. If 2 is included in as one of the prime numbers the sum of two prime numbers will be odd. (i.e 2+5=7)
True of false 0 is neither a postive or negative number?
True. All numbers can be either positive or negative with the exception of zero, which is neither.
What is the generalized formula for the number of consecutive integers in a set X to X+K
X+K-X+1=K+1.

The number of integers in a set is always the differences between both extremes plus 1.

For example:

How many integers are there from 14 to 765, inclusive?

Answer:

765-14+1=752
How do you find the sum of consecutive integers?
SUM = AVERAGE * NUMBER OF TERMS

1. Find the average.
2. Find the number of terms, which is the differences of the extremes plus 1.
3. Multiple the average and the number of terms to get the sum.

Example.

What is the sum of all integers from 20 to 100, inclusive?

1. Find the average, which is the middle term for a set of consecutive integers with an odd number of terms.

100+20=120/2=60 or 100-20+1=81 terms thus 40 terms from 20 is the middle. 40+20=60 is the middle term.

2. Number of terms = 100-20+1=81 terms.

3. Multiple the average by the number of terms yields sum.

SUM = AVERAGE * NUMBER OF TERMS

SUM = 60*81 = 4860
True or false the product of n consecutive terms is divisible by n
True.
21*22=462 is divisible by 2.
10*11*12=1320 is divisible by 3.
5*6*7*8= 1680 is divisible by 4.
1*2*3*4*5=120 is divisible by 5.

etc.

This rules applies to any number of consecutive terms.
True or false the sum of n consecutive terms ALWAYS divisible by n.
False.

This rule is only true if n is odd.

For any set of consecutive integers with an ODD number of terms, the sum of all the integers is always a multiple of the number of terms.

20+22+24=66 is divisible by 3.
10+11+12+13+14=60 is divisible by 5.


This works because of the following generalized rule. Consider the consecutive integer n, n+1, n+2.

Summing this we have n+n+1+n+2=3n+3 which is divisible by 3.

The same applies for any consecutive integer with an odd number of terms.
True or false is there is one even integer in a product of consecutive integer then the product is divisible by 2.
True.

If there is just one even integer in a set the product is divisible by 2.

If there is 2 even integers then the product is divisible by 4, etc.

Consider (x-1)x(x+1) with (x-1) being even which by definition means it's divisible by 2. Thus, we have even*odd*even=even hence because (x-1) is divisible by 2 thus x+1 must be even and also divisible by 2 thus the product of (x-1)x(x+1) must be divisible by 4.
What is 0^n if n is any real number
0.

0 to any power is 0 regardless of the exponent.
What is 1^n if n is any real number?
1.

1 to any power is 1 regardless of the exponent.
True or false x^n always increases if n--> infinity?
False.

If x is a fraction as n--> infinity x gets smaller or mathematically x--> 0
What is x^0?
1.

x raise to the power of 0 is by definition 1 regardless of the base.
SQRT(2)?
1.4
SQRT(3)?
1.7
SQRT(169)?
13
4^3
64
5^3
125
2^10
1024
2^5
32
3^3
27
3ROOT(27)
3
3ROOT(64)
4
3ROOT(125)
5
SQRT(5)
2.2
SQRT(7)
2.6
How do you determine is an integer is divisible by 7?
1. Split the numbers in groups of 3 starting from right to left.
2. Alternate between addition and subtraction of the numbers.
3. The output will have the same divisibility as the original numbers.

For example:

65,282,497

1. Splits the numbers starting from right to left into groups of 3.
497, 282, 65.

2. Alternate between addition and subtraction.

497-282+65 = 280.

3. 280 is divisible by 7 hence 65,282,497 is divisible by 7.
How do you calculate a checksum for addition.
1. Add the individual digits of the top number.
2. Add the individual digits of the botton number.
3. Add steps 1 and 2.
4. Add digits for sum of top and bottom number.
5. Compare.

For example:

95 = 5
42 = 6
12 = 3 (5+6+3=5)
---
149 = 5

5=5 correct
How do you calculate a checksum for multiplication.
1. Add digits of top term.
2. Add digits of bottom term.
3. Add digits of product of two terms.
4. Multiple step 2 by 3.
5. Compare results from step 3 to step 4.

Example:

33 =0
27 =0
---
891 =0

Correct
How do you determine if a number is divisible by 13?
1. Multiply the one's column by 9
2. Subtract the number with the one's colum deleted.

If this operation is divisible by 13 then the number is divisible by 13.

Example:

351
35-9*1=26

Since 26 is divisible by 13 then 359 is divisible by 13.
How do you determine if a number is divisible by 11?
1. Add the 1rst, 3rd, 5th etc digits of a number together.
2. Add the 2nd, 4th, 6th etc digits of a number together.
3. Subtract step 1 from 2.

If the result from step 3 is divisible by 11 the number is divisible by 11.

927454
1. 9+7+5 = 21
2. 2+4+4 = 10
3. 21-10=11, so 927454 is divisible by 11.