Prime numbers | Factors and multiples | Pre-Algebra | Khan Academy

Summary

This video introduces the concept of prime numbers, explaining that a prime number is a natural number divisible by exactly two natural numbers: itself and 1. Through several examples, the video illustrates which numbers are prime and which are not, highlighting how prime numbers serve as the 'building blocks' of numbers, similar to atoms in physics. The video also touches on how primes are important in areas like cryptography. Examples include the numbers 2, 3, 5, and 7, while larger numbers like 16 and 51 are shown to not be prime.

Takeaways

• 🔢 Prime numbers are natural numbers divisible by exactly two numbers: 1 and itself.
• 🧐 The smallest natural number, 1, is not a prime number because it is divisible by only one number, itself.
• ✔️ The number 2 is the only even prime number since it's divisible only by 1 and 2.
• 🔎 The number 3 is also a prime number because it is divisible only by 1 and 3.
• ❌ The number 4 is not prime because it is divisible by 1, 2, and 4.
• ✅ The number 5 is prime since it can only be divided by 1 and 5.
• 🔄 Numbers divisible by more than two natural numbers, like 6, are not prime.
• 💡 Prime numbers are building blocks of numbers, similar to how atoms are building blocks of matter.
• ❓ Larger numbers can be prime, like 17, which is divisible only by 1 and 17.
• ❌ The number 51 is not prime as it is divisible by 3 and 17, not just 1 and 51.

Q & A

What is the basic definition of a prime number?

A prime number is a natural number that is divisible by exactly two natural numbers: itself and 1.

Why is 1 not considered a prime number?

Although 1 is divisible by itself, it is only divisible by one natural number, not two, which is required for a number to be prime.

Why is 2 considered a special prime number?

2 is the only even prime number because it is divisible only by 1 and 2, while all other even numbers are divisible by 2 and other numbers.

Why is 4 not a prime number?

4 is divisible by 1, 2, and 4, meaning it has more than two divisors, which disqualifies it as a prime number.

How can prime numbers be thought of as the building blocks of numbers?

Prime numbers are similar to atoms in that they cannot be broken down into products of smaller natural numbers. Non-prime numbers, like 6, can be factored into primes (e.g., 6 = 2 x 3).

What makes 7 a prime number?

7 is divisible only by 1 and 7, and no other numbers, making it a prime number.

What is an example of a non-prime number with multiple divisors?

16 is not a prime number because it is divisible by 1, 2, 4, 8, and 16, meaning it has multiple divisors beyond just 1 and itself.

Is 17 a prime number? Why or why not?

Yes, 17 is a prime number because it is divisible only by 1 and 17, with no other divisors.

What makes 51 a non-prime number?

51 is not prime because it is divisible by 3 and 17, in addition to 1 and 51.

What is the importance of prime numbers in fields like cryptography?

Prime numbers are fundamental in cryptography because they serve as the basis for encryption algorithms that protect information in computing systems.