Fundamental theorem of arithmetic

High school (ages 12+)
Mathematics & Numbers

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Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/fundamental-theorem-of-arithmetic

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the formal proof origin?Carl Friedrich Gauss, 'Disquisitiones Arithmeticae', 1801
2. What is the abstract algebraic generalization?Unique Factorization Domains (UFDs), where elements have unique factorizations into irreducibles
3. What is the secret code of numbers?It is the unique list of prime numbers that multiply together to make the number. For example, 12 = 2 × 2 × 3.
4. How do we find the prime factors of a number?Keep dividing the number by the smallest prime until you can no longer divide. The remaining primes are the secret code.

Prime Number: An integer greater than 1 whose only positive divisors are 1 and itself.
Composite Number: An integer greater than 1 that is not prime; it has divisors other than 1 and itself.
Unique Factorization Domain (UFD): A commutative ring with unity where every non-zero, non-unit element has a unique prime factorization.