30030 has six prime numbers in its factorization (2x3x5x7x11x13).
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The first number with six distinct prime factors is:
2 x 3 x 5 x 7 x 11 x 13 = 30030
To find the prime factorization of a number: Begin by listing 2 numbers that will multiply to make your number. 6 = 2 * 3 Can we find 2 numbers to multiply to make 2, or 3? (aside from 1) No, of course not. In fact, 2 and 3 are prime. Once you have all primes, you can stop. 6 = 2 * 3 2 * 3 is the prime factorization of 6.
Prime Factorization of 84No, 7 X 12 is not the prime factorization of 84. In order to be prime factorization, all factors must be prime numbers. 7 is prime, but 12 is not. Since it is an even number, 2 will divide into it. 2 times 6 is 12, so the factorization would be 7 X 2 X 6. Since 6 is not a prime number, that is not the prime factorizatio of 84. The factors of 6 are 2 and 3. That means the factorization is 7 X 2 X 2 X 3. All the factors are now prime numbers, so the prime factorization of 84 with the factors in order from smallest to largest is 2 X 2 X 3 X 7. When finding the prime factorization of any number, you have to keep factoring any composite factors until all the factors are prime.
Prime factorization is a way of writing a composite number as the product of its prime factors. The prime factors of 6 are 2 and 3. 2 x 3 is the prime factorization of 6.
You find the prime factorization of 42 like this. You think what 2 number multiplied together give you 42: 6x7 7 is prime because the only factors it has is 1 and itself. 6 can be broken into 3x2. So you currently have 7x3x2. All these numbers are prime so you just found the prime factorization!
Draw the prime factorization table and put both the numbers on it. Find common prime factors and divide both of them writing the products down. Do this until the quotients are either 1 or any prime number. Write down all the factors used and it will be the prime factorization. Multiply them and you will find the LCM of the numbers. Here, 18,21 6,7...................(/3) Prime factorization=6*7*3 LCM=42*3=126