Prime factor of 36
To decompose the prime factor of 36, we need to know that 36 is a composite number, that is, it is not a prime number, so it can be decomposed into the product of several prime numbers. The prime factor of 36 is 2,2,3, that is, 36=2×2×3.
Steps to decompose prime factors
The following are the specific steps to decompose prime factors:
1. The number to be decomposed is expressed as the product of several prime numbers.
2. Starting from the smallest prime number 2, divide the number to be decomposed by 2. If it is divisible, continue to divide by 2 until it is not divisible.
3. Starting from 3, divide the number to be decomposed by 3. If it is divisible, continue to divide by 3 until it is not divisible.
4. And so on until the final quotient is a prime number.
5. Multiply all prime numbers to get the prime factor of the number to be decomposed.
Examples of factorizing prime factors
Take 72 as an example to introduce the specific steps of decomposing prime factors:
1. Express 72 as the product of several prime numbers, that is, 72=2×2×2×3×3.
2. Starting from the smallest prime number 2, divide 72 by 2 to get 36, continue to divide by 2 to get 18, and continue to divide by 2 to get 9. You can't divide by 2 at this time.
3. Next, starting from 3, divide 9 by 3 to get 3. The quotient obtained at this time is a prime number, so the decomposition is completed.
4. Multiply all prime numbers to get a prime factor of 72, that is, 72=2×2×2×3×3.
Application of factorization prime factor
Prime factorization is not only the basic knowledge in mathematics, but also widely used, such as finding the greatest common divisor and the least common multiple.
Taking the greatest common divisor as an example, if we need the greatest common divisor of 36 and 48, we can first decompose 36 and 48 into prime factors to get 36=2×2×3×3, 48 = 2×2×2×3, and then multiply their common prime factors, that is, 2× 2× 3 = 65438+.