The answer is: 5 x 5 x 7 x 7 = 1,225
The prime factorization of 225 is (3^2 \times 5^2). To express this as a product of four prime numbers, we can write it as (3 \times 3 \times 5 \times 5). Thus, the four prime numbers that multiply to make 225 are 3, 3, 5, and 5.
They are: 7 times 13 = 91
The prime factorization of 105 is (3 \times 5 \times 7). To express this as a product of four prime numbers, we can include 1 as a prime number (though technically, 1 is not prime), yielding the combination (1 \times 3 \times 5 \times 7 = 105). However, if strictly considering only primes, the prime factors are 3, 5, and 7, which multiply to give 105. Therefore, there are not four distinct prime numbers that multiply to make 105.
The prime factorization of 735 is (3 \times 5 \times 7 \times 7). However, since 7 is repeated, it does not constitute four distinct prime numbers. The four prime numbers that multiply to give 735, including repetition, are 3, 5, and two instances of 7. Thus, the prime numbers are 3, 5, 7, and 7.
They are: 1 times 19 = 19 which is a prime number
Three times three times three.
The prime factorization of 225 is (3^2 \times 5^2). To express this as a product of four prime numbers, we can write it as (3 \times 3 \times 5 \times 5). Thus, the four prime numbers that multiply to make 225 are 3, 3, 5, and 5.
They are: 7 times 13 = 91
The prime factorization of 105 is (3 \times 5 \times 7). To express this as a product of four prime numbers, we can include 1 as a prime number (though technically, 1 is not prime), yielding the combination (1 \times 3 \times 5 \times 7 = 105). However, if strictly considering only primes, the prime factors are 3, 5, and 7, which multiply to give 105. Therefore, there are not four distinct prime numbers that multiply to make 105.
The prime factorization of 735 is (3 \times 5 \times 7 \times 7). However, since 7 is repeated, it does not constitute four distinct prime numbers. The four prime numbers that multiply to give 735, including repetition, are 3, 5, and two instances of 7. Thus, the prime numbers are 3, 5, 7, and 7.
They are: 1 times 19 = 19 which is a prime number
They are 1 times 19 = 19 which is a prime number
There are no three prime numbers that multiply to exactly 100, as 100 can be factored into its prime components, which are 2 and 5. The prime factorization of 100 is (2^2 \times 5^2), meaning it only consists of the primes 2 and 5. Since prime numbers must be distinct and cannot be repeated in this context, it is impossible to find three prime numbers that multiply to 100.
There are no two prime numbers that multiply to 24. You need four numbers (even though one appears 3 times).
The four prime numbers that multiply to make 315 are 3, 3, 5, and 7. Specifically, 315 can be factored as (3^2 \times 5 \times 7). Thus, the prime factors include the repeated prime number 3 along with 5 and 7.
They are: 1 times 107 = 107 which is also a prime number
Only once - thanks to the unique prime factorisation theorem.