134 LearnersLast updated on May 26th, 2025
Is 478 a Prime Number?
The numbers that have only two factors, which are 1 and themselves, are called prime numbers. For encryption, computer algorithms, and barcode generation, prime numbers are used. In this topic, we will be discussing whether 478 is a prime number or not.
Is 478 a Prime Number?
There are two types of numbers, mostly —
Prime numbers and composite numbers, depending on the number of factors.
A prime number is a natural number that is divisible only by 1 and itself.
For example, 3 is a prime number because it is divisible by 1 and itself.
A composite number is a positive number that is divisible by more than two numbers.
For example, 6 is divisible by 1, 2, 3, and 6, making it a composite number.
Prime numbers follow a few properties like:
- Prime numbers are positive numbers always greater than 1.
- 2 is the only even prime number.
- They have only two factors: 1 and the number itself.
- Any two distinct prime numbers are co-prime numbers because they have only one common factor, which is 1.
As 478 has more than two factors, it is not a prime number.
Why is 478 Not a Prime Number?
The characteristic of a prime number is that it has only two divisors: 1 and itself.
- Since 478 has more than two factors, it is not a prime number.
- A few methods are used to distinguish between prime and composite numbers.
These methods include:
- Counting Divisors Method
- Divisibility Test
- Prime Number Chart
- Prime Factorization
Using the Counting Divisors Method
The method in which we count the number of divisors to categorize the numbers as prime or composite is called the counting divisors method. Based on the count of the divisors, we categorize prime and composite numbers.
- If there is a total count of only 2 divisors, then the number would be prime.
- If the count is more than 2, then the number is composite.
Let’s check whether 478 is prime or composite.
Step 1: All numbers are divisible by 1 and themselves.
Step 2: Divide 478 by 2. It is divisible by 2, so 2 is a factor of 478.
Step 3: Divide 478 by 3. It is not divisible by 3, so 3 is not a factor of 478.
Step 4: You can simplify checking divisors up to 478 by finding the root value. We then need to only check divisors up to the root value. Step 5: When we divide 478 by 2, 239, and other numbers up to its square root, it is divisible by 2.
Since 478 has more than 2 divisors, it is a composite number.
Using the Divisibility Test Method
We use a set of rules to check whether a number is divisible by another number completely or not. It is called the Divisibility Test Method.
Divisibility by 2: The number in the one's place value is 8. Eight is an even number, which means that 478 is divisible by 2.
Divisibility by 3: The sum of the digits in the number 478 is 19. Since 19 is not divisible by 3, 478 is also not divisible by 3.
Divisibility by 5: The unit’s place digit is 8. Therefore, 478 is not divisible by 5.
Divisibility by 7: The last digit in 478 is 8. To check divisibility by 7, double the last digit (8 × 2 = 16). Then, subtract it from the rest of the number (47 - 16 = 31). Since 31 is not divisible by 7, 478 is also not divisible by 7.
Divisibility by 11: In 478, the sum of the digits in odd positions is 12, and the sum of the digits in even positions is 7. The difference is 5, which is not divisible by 11. Since 478 is divisible only by 2 and 239, it has more than two factors.
Therefore, it is a composite number.
Using Prime Number Chart
The prime number chart is a tool created by using a method called “The Sieve of Eratosthenes.”
In this method, we follow the following steps.
Step 1: Write 1 to 100 in 10 rows and 10 columns.
Step 2: Leave 1 without coloring or crossing, as it is neither prime nor composite.
Step 3: Mark 2 because it is a prime number and cross out all the multiples of 2.
Step 4: Mark 3 because it is a prime number and cross out all the multiples of 3.
Step 5: Repeat this process until you reach the table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers from 1 to 100.
The list is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
478 is not present in the list of prime numbers, so it is a composite number.
Using the Prime Factorization Method
Prime factorization is a process of breaking down a number into prime factors. Then, multiply those factors to obtain the original number.
Step 1: We can write 478 as 2 × 239.
Step 2: Both 2 and 239 are prime numbers.
Therefore, the prime factorization of 478 is 2 × 239.
Common Mistakes to Avoid When Determining if 478 is Not a Prime Number
Children might have some misconceptions about prime numbers when they are learning about them. Here are some mistakes that might be made by children.
Mistake 1
Assuming That All Odd Numbers Are Prime
Children often assume that all odd numbers are prime numbers. They should be taught that except for 2, most prime numbers are odd but not all odd numbers are prime.
For example, 15 is an odd number, but it has more than two factors, which makes it a composite number.
Mistake 2
Confusing 1 as a Prime Number
Children should know the definition of a prime number as having only two factors. But 1 has only one factor, which is itself. 1 is a unique number that is neither a prime nor a composite number.
Mistake 3
Depending Too Much on Memorization
Children rely on memorizing the prime numbers. But they might forget whether 29 or 39 is prime. To avoid these kinds of problems, children should have knowledge of divisibility rules rather than depending on memorization.
Mistake 4
Applying Divisibility Rules Incorrectly
When children divide a number by another number, they might make mistakes in calculation.
For example, children might make mistakes while dividing 72 by 3. Teach them shortcuts, like if the sum of the digits of a number is divisible by 3 then the number is also divisible by 3.
Mistake 5
Assuming That Negative Numbers Are Prime
Children might think that negative numbers can also be prime numbers. They might apply the divisibility rule of 2 for -48 to check whether it is prime or not. They need to know that prime numbers are positive numbers greater than 1.
FAQ on is 478 a Prime Number?
1.Is 478 a perfect square?
2.What is the sum of the divisors of 478?
3.What are the factors of 478?
4.What are the closest prime numbers to 478?
5.What is the prime factorization of 478?
6.How can children in India use numbers in everyday life to understand Is 478 a Prime Number??
7.What are some fun ways kids in India can practice Is 478 a Prime Number? with numbers?
8.What role do numbers and Is 478 a Prime Number? play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Is 478 a Prime Number? skills?
Important Glossaries for "Is 478 a Prime Number"
- Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 478 is a composite number because it is divisible by 1, 2, 239, and 478.
- Prime numbers: Numbers greater than 1 that have no divisors other than 1 and themselves. For example, 3 and 5 are prime numbers.
- Divisibility Test: A method to determine if a number is divisible by another without performing full division.
- Prime Factorization: The process of expressing a number as the product of its prime factors.
- Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.
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About BrightChamps in India
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
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