Prime Factorization, GCF and LCM
Complete prime factorization on the number 75
75 = 31 X 52
Complete the operation 0.13 X 1.45
0.13 × 1.45 = 0.1885
A fish tank has a length of 4 feet, a width of 6 inches, and a height of 5 feet. What is the volume of the fish tank, in cubic feet?
First, convert the width of 6 inches into 0.5 feet
Volume = 4 feet X 0.5 feet X 5 feet = 10 feet3
What is 35% of 105?
10% = 10.5
10% = 10.5
10% = 10.5
5% = 5.25
Adding, 35% = 36.75
The number 9,00x is divisible by 4, where x is the units digit. What are all possible values that x could be?
The last two digits has to be a multiple of 4, so x = 0, 4 or 8
Complete prime factorization on the number 102
102 = 21 X 31 X 171
Complete the operation 0.04 X 0.4 X 4.0
0.04 × 0.4 × 4.0 = 0.016 × 4.0 = 0.064
A rectangle has a perimeter of 24 yards. What is the greatest possible area that the rectangle can have?
The greatest possible area is in a square, so the rectangle can be a square with side length 6 yards, which has an area of 6 yards X 6 yards = 36 yards2. Note that the answer needs to include units, either square yards or yards2!
What is 20% of 40% of 60?
10% of 60 is 6, so 40% of 60 is 4 X 6 = 24
Then 10% of 24 is 2.4, so 20% is 2.4 X 2 = 4.8
The number 86x is divisible by 3, where x is the units digit. What are all possible values that x could be?
8 + 6 + x has to be a multiple of 3, so 14 + x has to be a multiple of 3
So x = 1, 4, or 7
What is the sum of all of the prime numbers between 0 and 10 (including both numbers)?
The prime numbers between 0 and 10 (inclusive) are 2, 3, 5 and 7. The sum is 2 + 3 + 5 + 7 = 17
Complete the operation 5.62 ÷ 0.05
5.62 ÷ 0.05 = 112.4
A fair coin is equally likely to land Heads as it is to land Tails. What is the probability (expressed as a fraction) of the coin landing Tails three straight times?
There are 8 possibilities for three coin flips:
HHH HHT HTH HTT
THH THT TTH TTT
Then the probability is 1/8
Alternatively, each coin toss has P(Tails) = 1/2 , and so P(three Tails in a row) = 1/2 X 1/2 X 1/2 = 1/8
Rounded to the nearest whole number percent, 80 is what percent of 180?
Translating into an algebraic expression,
80 = n% X 180
n% = 80/180 = 8/18 = 4/9 = 0.444….
Rounding to the nearest percent gives 44%
Is the number 52,052,052,052 divisible by 3, 6, and/or 9?
The sum of the digits is 5(4) + 2(4) = 20 + 4 = 26, which is not divisible by 3 or 9. Since it is not divisible by 3, it is not divisible by 6 either.
Therefore, this number is not divisible by any of 3, 6 or 9.
What is the sum of all of the prime numbers between 10 and 20 (including both numbers)?
The prime numbers between 10 and 20 (inclusive) are 11, 13, 17 and 19. The sum is 11 + 13 + 17 + 19 = 60
Complete the operation 27.5 X 1.62
27.5 X 1.62 = 44.55
How many ways are there to re-arrange the letters in the word MATH (for example, MATH and ATMH are two ways)?
There are 4 ways to re-arrange the first letter, then 3 ways to re-arrange the second letter, then 2 ways to re-arrange the third letter and 1 way to re-arrange the fourth letter.
Then 4 X 3 X 2 X 1 = 24 ways
This can be written out as well, notice that there are 6 ways to write out the word that begin with an M
MATH, MAHT, MTAH, MTHA, MHAT, MHTA
If there are 6 ways for starting with M, then there are 6 ways for each starting letter, and 6 X 4 = 24 ways
500 is increased by 150%. What number does it increase to?
150% of 500 is 750
Therefore, the number increases to 500 + 750 = 1,250.
Start off with a sum of zero. If the number 564 is divisible by 2, add 2 to the sum. If the number 564 is divisible by 3, add 3 to the sum. If the number 564 is divisible by 4, add 4 to the sum…keep on going until, if the number 564 is divisible by 10, add 10 to the sum. What is the total sum after checking all of the divisibility rules between 2 and 10?
564 --> is divisible by 2, since it is even. Therefore, sum = 0 + 2 = 2
564 --> is divisible by 3, since the digits sum to 5+6+4 = 15 which is divisible by 3. Therefore, sum = 2 + 3 = 5
564 --> is divisible by 4, since 64 is divisible by 4. Therefore, sum = 5 + 4 = 9
564 --> is not divisible by 5, since it does not end in a 5 nor a 0
564 --> is divisible by 6, because it is divisible by both 2 and 3. Therefore, sum = 9 + 6 = 15
564 --> is not divisible by 7, you can check this with long division since we did not learn the rule for 7.
564 --> is not divisible by 8, since 560 8 = 70, so the next number that is divisible by 8 after 560 is 568
564 --> is not divisible by 9, since the digits sum to 5+6+4 = 15 which is not divisible by 9.
564 --> is not divisible by 10, since it does not end in a 0
Then the overall sum is 15 (divisible by 2, 3, 4 and 6).
What is the Greatest Common Factor of 104 and 106?
104 = 23 X 131
106 = 21 X 531
GCF = common factors = 2
Complete the operation 28.1 × 0.1 ÷ 0.007, and round to the nearest whole number.
28.1 × 0.1 ÷ 0.007 = 2.81 ÷ 0.007 ≈ 401.43 ≈ 401
How many ways are there to re-arrange the letters in the word EVEN (for example, EVEN and EVNE are two ways)?
We found in Problem #400 that there are 24 ways for MATH, but now there are half the number of combinations, because for every combination, the E’s can be flipped.
For example, E1VE2N is the same as E2VE1N
So, 24 / 2 = 12 ways
12.5% of a number is 250. What is the number?
Translating into an algebraic expression,
12.5% X n = 250
1/8 X n = 250
n = 2,000
How many three-digit numbers are divisible by three?
First, how many numbers there are between 0 and 999 that are divisible by three
999 / 3 = 333, so there are 333 numbers between 0 and 999 that are divisible by three
Then, find out how many numbers there are between 0 and 99 that are divisible by three
99 / 3 = 33, so there are 33 numbers between 0 and 99 that are divisible by three
Then, 333 – 33 = 300 numbers