Exercis 2.5 1. Express each of the following numbers as prime factorization form. a. 21 b. 70 c. 105 d. 252 e. 360 f. 1,848 2. 180 can be written as 2^atimes 3^btimes 5^c .Then, find the value of a,b and c. 3. Find the four prime numbers whose product is 462.

1. Express each of the following numbers factorization form:<br />a. 21 = 3 × 7<br />b. 70 = 2 × 5 × 7<br />c. 105 = 3 × 5 × 7<br />d. 252 = 2^2 × 3^2 × 7<br />e. 360 = 2^3 × 3^2 × 5<br />f. 1,848 = 2^3 × 3 × 7^2<br /><br />2. 180 can be written as $2^{a}\times 3^{b}\times 5^{c}$. Then, find the value of a, b, and c.<br />To express 180 in the form $2^{a}\times 3^{b}\times 5^{c}$, we need to find the prime factors of 180 and their respective exponents.<br />The prime factorization of 180 is 2^2 × 3^2 × 5.<br />Therefore, the values of a, b, and c are:<br />a = 2<br />b = 2<br />c = 1<br /><br />3. Find the four prime numbers whose product is 462.<br />To find the four prime numbers whose product is 462, we need to find the prime factors of 462.<br />The prime factorization of 462 is 2 × 3 × 7 × 23.<br />Therefore, the four prime numbers whose product is 462 are 2, 3, 7, and 23.