How to factor a number - ISEE Upper Level Quantitative Reasoning
Card 1 of 240
Which of these numbers is relatively prime with 18?
Which of these numbers is relatively prime with 18?
Tap to reveal answer
For two numbers to be relatively prime, they cannot have any factor in common except for 1. The factors of 18 are 1, 2, 3, 6, 9, and 18.
We can eliminate 32 and 34, since each shares with 18 a factor of 2; we can also eliminate 33 and 39, since each shares with 18 a factor of 3. The factors of 35 are 1, 5, 7, and 35; as can be seen by comparing factors, 18 and 35 only have 1 as a factor, making 35 the correct choice.
For two numbers to be relatively prime, they cannot have any factor in common except for 1. The factors of 18 are 1, 2, 3, 6, 9, and 18.
We can eliminate 32 and 34, since each shares with 18 a factor of 2; we can also eliminate 33 and 39, since each shares with 18 a factor of 3. The factors of 35 are 1, 5, 7, and 35; as can be seen by comparing factors, 18 and 35 only have 1 as a factor, making 35 the correct choice.
← Didn't Know|Knew It →
Which of the following is the prime factorization of 333?
Which of the following is the prime factorization of 333?
Tap to reveal answer
To find the prime factorization, break the number down as a product of factors, then keep doing this until all of the factors are prime.
To find the prime factorization, break the number down as a product of factors, then keep doing this until all of the factors are prime.
← Didn't Know|Knew It →
What is the sum of all of the factors of 27?
What is the sum of all of the factors of 27?
Tap to reveal answer
27 has four factors: 
Their sum is 
.
27 has four factors:
Their sum is
← Didn't Know|Knew It →
Give the prime factorization of 91.
Give the prime factorization of 91.
Tap to reveal answer
Both are prime factors so this is the prime factorization.
Both are prime factors so this is the prime factorization.
← Didn't Know|Knew It →
Add all of the factors of 30.
Add all of the factors of 30.
Tap to reveal answer
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. Their sum is
.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. Their sum is
← Didn't Know|Knew It →
How many factors does 40 have?
How many factors does 40 have?
Tap to reveal answer
40 has as its factors 1, 2, 4, 5, 8, 10, 20, and 40 - a total of eight factors.
40 has as its factors 1, 2, 4, 5, 8, 10, 20, and 40 - a total of eight factors.
← Didn't Know|Knew It →
Which is the greater quantity?
(a) The number of factors of 15
(b) The number of factors of 17
Which is the greater quantity?
(a) The number of factors of 15
(b) The number of factors of 17
Tap to reveal answer
(a) 15 has four factors, 1, 3, 5, and 15.
(b) 17, as a prime, has two factors, 1 and 17.
Therefore, (a) is greater.
(a) 15 has four factors, 1, 3, 5, and 15.
(b) 17, as a prime, has two factors, 1 and 17.
Therefore, (a) is greater.
← Didn't Know|Knew It →
Which is the greater quantity?
(a) The number of factors of 169
(b) The number of factors of 121
Which is the greater quantity?
(a) The number of factors of 169
(b) The number of factors of 121
Tap to reveal answer
Each number has only three factors. 121 has 1, 11, and 121 as factors; 169 has 1, 13, and 169 as factors. The answer is that the quantities are equal.
Each number has only three factors. 121 has 1, 11, and 121 as factors; 169 has 1, 13, and 169 as factors. The answer is that the quantities are equal.
← Didn't Know|Knew It →
Which is the greater quantity?
(a) The product of the integers between 
and 
inclusive
(b) The sum of the integers between 
and 
inclusive
Which is the greater quantity?
(a) The product of the integers between
(b) The sum of the integers between
Tap to reveal answer
The quanitites are equal, as both can be demonstrated to be equal to 
.
(a) One of the integers in the given range is , so one of the factors will be , making the product .
(b) The sum of the numbers will be:
The quanitites are equal, as both can be demonstrated to be equal to .
(a) One of the integers in the given range is , so one of the factors will be
, making the product
.
(b) The sum of the numbers will be:
← Didn't Know|Knew It →
Which is the greater quantity?
(a) The sum of the factors of 
(b) The sum of the factors of 
Which is the greater quantity?
(a) The sum of the factors of
(b) The sum of the factors of
Tap to reveal answer
(a) The factors of 
are 
Their sum is
.
(b) The factors of 
are 
Their sum is
.
(b) is greater.
(a) The factors of
(b) The factors of
(b) is greater.
← Didn't Know|Knew It →
Which is the greater quantity?
(a) The sum of all of the two-digit even numbers
(b) 2,500
Which is the greater quantity?
(a) The sum of all of the two-digit even numbers
(b) 2,500
Tap to reveal answer
The sum of the integers from 
to 
is equal to 
. We take advantage of the fact that the sum of the even numbers from 10 to 98 is equal to twice the sum of the integers from 5 to 49, as seen here:
The sum of the integers from
← Didn't Know|Knew It →
What is the prime factorization of 
?
What is the prime factorization of
Tap to reveal answer
First make a factor tree for 16. Keep breaking it down until you get all prime numbers (for example: 
, which then yields 
). Then, at the end, remember to factor the variables as well. Since the b term is squared, that means there are two of them. Therefore, the final answer is 
.
First make a factor tree for 16. Keep breaking it down until you get all prime numbers (for example:
← Didn't Know|Knew It →
Which one is greater?
The total number of factors of 
Which one is greater?
Tap to reveal answer
Factors of 
are:
. So it has 
factors, which is less than 
.
Factors of
← Didn't Know|Knew It →
Which one is greater?
number of factors of 
Which one is greater?
Tap to reveal answer
Factors of 
are:
. So it has 
factors which is less than 
.
Factors of
← Didn't Know|Knew It →
Which one is greater?
The sum of all of the factors of 
Which one is greater?
Tap to reveal answer
Factors of 
are:
. So we can write:
Factors of
← Didn't Know|Knew It →
Which one is the greater quantity:
Sum of the factors of 
Sum of the factors of 
Which one is the greater quantity:
Tap to reveal answer
Factors of 
are:
and their summation is:
and the factors of 
are:
and their summation is:
So 
is greater than 
.
Factors of
and the factors of
So
← Didn't Know|Knew It →
Which one is greater?
The number of factors of 
The number of factors of 
Which one is greater?
Tap to reveal answer
has only three factors of 
and
also has three factors of 
So the number of their factors are the same
and
So the number of their factors are the same
← Didn't Know|Knew It →
Which one is greater?
The number of factors of 
The number of factors of 
Which one is greater?
Tap to reveal answer
The factors of 
are 
. So 
has ten factors.
The factors of 
are 
. So 
has eight factors.
So 
is greater than 
.
The factors of
The factors of
So
← Didn't Know|Knew It →
Which one is greater?
The sum of the factors of 
The sum of the factors of 
Which one is greater?
Tap to reveal answer
Factors of 
are: 
Factors of 
are: 
So 
is greater than 
Factors of
Factors of
So
← Didn't Know|Knew It →
Which one is greater?
The sum of the factors of 
The product of the factors of 
Which one is greater?
Tap to reveal answer
Factors of 
are 
Factors of 
are 
So 
is greater thaan 
.
Factors of
Factors of
So
← Didn't Know|Knew It →