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Quizzes > High School Quizzes > Mathematics

4th Grade Factors and Multiples Practice Quiz

Interactive worksheet challenges for Class 6 learners

Difficulty: Moderate
Grade: Grade 4
Study OutcomesCheat Sheet
Colorful paper art promoting Factors and Multiples Magic, a math quiz for middle school students.

Easy
Which of the following is a factor of 24?
7
4
9
5
4 is a factor of 24 because 24 divided by 4 equals 6, which is an integer. The other options do not divide 24 evenly.
Which number is a multiple of 5?
23
21
27
20
20 is a multiple of 5 because 20 equals 5 multiplied by 4. The other numbers are not obtained by multiplying 5 by an integer.
What is the greatest factor common to both 12 and 18?
3
9
6
4
6 is the greatest common factor of 12 and 18 since both numbers can be divided evenly by 6. The other options are either smaller common factors or do not divide both numbers.
Which of the following numbers is a prime number?
27
15
11
21
11 is a prime number because its only divisors are 1 and itself. The other numbers have additional divisors, making them composite.
Which number is both a factor of 30 and a multiple of 5?
5
6
3
2
5 is both a factor of 30, since 30 divided by 5 is 6, and a multiple of 5, as 5 equals 5 multiplied by 1. The other numbers do not satisfy both conditions simultaneously.
Medium
What is the Least Common Multiple (LCM) of 4 and 6?
24
18
8
12
The LCM of 4 and 6 is 12 because it is the smallest number that both 4 and 6 divide evenly into. The other options are either too large or not common multiples of both numbers.
What is the Greatest Common Divisor (GCD) of 42 and 56?
21
14
7
28
The GCD of 42 and 56 is 14 because it is the largest number that divides both 42 and 56 without a remainder. The other options do not evenly divide both numbers or are not the greatest common divisor.
Which of the following numbers is a composite number?
9
11
13
17
9 is composite because it has divisors other than 1 and itself (specifically, 3 is a divisor twice). The other numbers are prime, having only two distinct factors.
How many factors does the number 28 have?
8
7
6
5
The factors of 28 are 1, 2, 4, 7, 14, and 28, which add up to 6 factors in total. This is determined by listing all positive divisors of 28.
Which number is a multiple of both 3 and 4?
8
10
12
9
12 is a multiple of both 3 and 4 since 12 equals 3 multiplied by 4 and also 4 multiplied by 3. The other options do not satisfy the condition of being divisible by both numbers.
What is the LCM of 8 and 12?
12
20
24
16
The smallest common multiple of 8 and 12 is 24, since both numbers divide evenly into 24. The other options either do not meet the criteria or are not the least common multiple.
Which of these numbers is not a multiple of 6?
24
30
18
13
13 is not a multiple of 6 because it cannot be written as 6 times an integer. The other numbers are clearly multiples of 6.
Select the statement that accurately describes factors.
A factor is always greater than the original number.
A factor must be a prime number always.
A factor is a number that can only be multiplied, not divided.
A factor divides a number without leaving a remainder.
A factor is defined as a number that divides another number evenly, with no remainder, which is exactly what the first option states. The other statements provide incorrect or misleading descriptions of factors.
Select the statement that correctly describes multiples.
A multiple is the product of a number and any integer.
A multiple is a number that adds another number.
A multiple divides the original number exactly.
A multiple is always smaller than the original number.
Multiples are generated by multiplying a given number by any integer, which is accurately stated in the first option. The other options misrepresent the concept of multiples.
If a number has exactly 3 positive factors, which of the following must be true about the number?
It is an even number.
It is a prime number.
It is a perfect square of a prime number.
It is a composite number.
A number with exactly 3 positive factors is the square of a prime number because its only factors are 1, the prime itself, and the square. This unique property confirms that the correct answer is the first option.
Hard
Among the factor pairs of 24, which pair has a sum of 10?
(4, 6)
(1, 24)
(3, 8)
(2, 12)
The factor pair (4, 6) adds up to 10 since 4 + 6 equals 10. The other pairs have sums that differ from 10, making (4, 6) the only correct answer.
If the product of the positive factors of 12 is 1728, what is the sum of its factors?
28
32
30
24
The factors of 12 are 1, 2, 3, 4, 6, and 12, and when added, they sum to 28. This is consistent with the fact that the product of these factors is 1728, confirming the correct sum.
A number is chosen at random from the set of factors of 60. What is the probability that this number is a multiple of 5?
1/2
1/4
2/3
1/3
There are 12 factors of 60, and 6 of these are multiples of 5, yielding a probability of 6/12 which simplifies to 1/2. This confirms that the correct probability is 1/2.
If the LCM of two numbers is 60 and their GCD is 2, which of the following could be one of the numbers?
15
20
30
10
Using the relationship that the product of two numbers equals the product of their LCM and GCD, one valid pair is 10 and 12. In this pair, the GCD is 2 and the LCM is 60, which makes 10 a correct choice.
Given that every prime factor of a number n is also a prime factor of 36, which of the following could n be?
20
14
25
18
The prime factors of 36 are 2 and 3, so any number n that only includes these primes qualifies. 18, which factors as 2 x 3², meets this condition, making it the correct answer.
0
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Study Outcomes

  1. Analyze numerical expressions to identify factors.
  2. Apply divisibility rules to determine multiples.
  3. Synthesize techniques for finding common factors and multiples.
  4. Evaluate problem-solving strategies for factor and multiple challenges.
  5. Develop logical reasoning to construct effective mathematical solutions.

Factors & Multiples Quiz: Grade 4 & 6 Cheat Sheet

  1. Understanding Factors - Factors are like the secret agents of a number that divide it without leaving any clues (remainders). For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, which form a neat division squad. Seeing factors in action helps you decode bigger problems with ease! Grab a factors worksheet
  2. Identifying Multiples - Multiples are like an endless parade: you start with a number and keep adding it again and again. For 5, the parade lineup is 5, 10, 15, 20, and so on, marching forever. Spotting multiples makes pattern hunting a breeze! Try some multiples worksheets
  3. Prime Numbers - Prime numbers are the cool loners of the number world because they only have 1 and themselves as factors. Think 2, 3, 5, 7, 11… they're like the VIPs at a party who don't mingle. Learning primes boosts your number-smashing superpowers! Explore prime practice
  4. Composite Numbers - Composite numbers are social butterflies - they mingle with more than two factors. Take 4: it chats with 1, 2, and 4, and there are tons more examples to explore. Breaking composites helps you prep for prime factorization puzzles! Dive into composite challenges
  5. Greatest Common Factor (GCF) - The GCF is the biggest buddy two numbers share in common. To find it, list all factors of each number and pick the largest match - it's like finding the perfect teammate. Mastering GCF makes simplifying fractions a walk in the park! Find GCF drills
  6. Least Common Multiple (LCM) - The LCM is the smallest party venue that both numbers can fit into without bumping heads. List multiples of each number and choose the tiniest one they both attend. LCM skills come in handy for adding fractions and scheduling fun! Practice LCM problems
  7. Divisibility Rules - Divisibility rules are your quick-fire cheats for checking if one number can go into another without dividing. For instance, if a number ends in an even digit, it's divisible by 2 - no long division needed! Memorizing these rules saves you tons of time on tests. Learn divisibility tips
  8. Factor Trees - A factor tree is a branching adventure that breaks a number down into its prime roots. For example, 18 splits into 2 × 3 × 3 in a neat tree diagram. Drawing factor trees turns complex numbers into easy-to-digest pieces! Build your own factor trees
  9. Common Multiples - Common multiples are the shared stops where two numbers meet on their endless number highway. For 3 and 4, the shared stops are 12, 24, 36, and so on. Spotting these helps with rhythm in equations and real-world planning! Check out common multiples
  10. Practice with Worksheets - Engaging with worksheets turns theory into hands-on fun, letting you flex your factors and multiples muscles. Try exercises that cover everything from basic factors to GCF and LCM challenges. Regular practice is the secret sauce for math mastery! Start your worksheet practice
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