To solve the problem, we will follow these steps:
### Step 1: Identify the prime factorization
The prime factorization of the number is given as \(2 \times 5 \times 7\).
### Step 2: Calculate the number
To find the number, we need to multiply the prime factors together:
\[
x = 2 \times 5 \times 7
\]
Calculating this step-by-step:
- First, multiply \(2\) and \(5\):
\[
2 \times 5 = 10
\]
- Next, multiply the result by \(7\):
\[
10 \times 7 = 70
\]
Thus, the number is \(70\).
### Step 3: Find all factors of the number
To find all factors of \(70\), we need to identify all integers that divide \(70\) without leaving a remainder. We can do this by checking integers from \(1\) to \(70\):
- \(1\) (since \(70 \div 1 = 70\))
- \(2\) (since \(70 \div 2 = 35\))
- \(3\) (not a factor, \(70 \div 3\) is not an integer)
- \(4\) (not a factor, \(70 \div 4\) is not an integer)
- \(5\) (since \(70 \div 5 = 14\))
- \(6\) (not a factor, \(70 \div 6\) is not an integer)
- \(7\) (since \(70 \div 7 = 10\))
- \(8\) (not a factor, \(70 \div 8\) is not an integer)
- \(9\) (not a factor, \(70 \div 9\) is not an integer)
- \(10\) (since \(70 \div 10 = 7\))
- \(11\) (not a factor, \(70 \div 11\) is not an integer)
- \(12\) (not a factor, \(70 \div 12\) is not an integer)
- \(13\) (not a factor, \(70 \div 13\) is not an integer)
- \(14\) (since \(70 \div 14 = 5\))
- \(15\) (not a factor, \(70 \div 15\) is not an integer)
- \(16\) (not a factor, \(70 \div 16\) is not an integer)
- \(17\) (not a factor, \(70 \div 17\) is not an integer)
- \(18\) (not a factor, \(70 \div 18\) is not an integer)
- \(19\) (not a factor, \(70 \div 19\) is not an integer)
- \(20\) (not a factor, \(70 \div 20\) is not an integer)
- \(21\) (not a factor, \(70 \div 21\) is not an integer)
- \(22\) (not a factor, \(70 \div 22\) is not an integer)
- \(23\) (not a factor, \(70 \div 23\) is not an integer)
- \(24\) (not a factor, \(70 \div 24\) is not an integer)
- \(25\) (not a factor, \(70 \div 25\) is not an integer)
- \(26\) (not a factor, \(70 \div 26\) is not an integer)
- \(27\) (not a factor, \(70 \div 27\) is not an integer)
- \(28\) (not a factor, \(70 \div 28\) is not an integer)
- \(29\) (not a factor, \(70 \div 29\) is not an integer)
- \(30\) (not a factor, \(70 \div 30\) is not an integer)
- \(31\) (not a factor, \(70 \div 31\) is not an integer)
- \(32\) (not a factor, \(70 \div 32\) is not an integer)
- \(33\) (not a factor, \(70 \div 33\) is not an integer)
- \(34\) (not a factor, \(70 \div 34\) is not an integer)
- \(35\) (since \(70 \div 35 = 2\))
- \(36\) (not a factor, \(70 \div 36\) is not an integer)
- \(37\) (not a factor, \(70 \div 37\) is not an integer)
- \(38\) (not a factor, \(70 \div 38\) is not an integer)
- \(39\) (not a factor, \(70 \div 39\) is not an integer)
- \(40\) (not a factor, \(70 \div 40\) is not an integer)
- \(41\) (not a factor, \(70 \div 41\) is not an integer)
- \(42\) (not a factor, \(70 \div 42\) is not an integer)
- \(43\) (not a factor, \(70 \div 43\) is not an integer)
- \(44\) (not a factor, \(70 \div 44\) is not an integer)
- \(45\) (not a factor, \(70 \div 45\) is not an integer)
- \(46\) (not a factor, \(70 \div 46\) is not an integer)
- \(47\) (not a factor, \(70 \div 47\) is not an integer)
- \(48\) (not a factor, \(70 \div 48\) is not an integer)
- \(49\) (not a factor, \(70 \div 49\) is not an integer)
- \(50\) (not a factor, \(70 \div 50\) is not an integer)
- \(51\) (not a factor, \(70 \div 51\) is not an integer)
- \(52\) (not a factor, \(70 \div 52\) is not an integer)
- \(53\) (not a factor, \(70 \div 53\) is not an integer)
- \(54\) (not a factor, \(70 \div 54\) is not an integer)
- \(55\) (not a factor, \(70 \div 55\) is not an integer)
- \(56\) (not a factor, \(70 \div 56\) is not an integer)
- \(57\) (not a factor, \(70 \div 57\) is not an integer)
- \(58\) (not a factor, \(70 \div 58\) is not an integer)
- \(59\) (not a factor, \(70 \div 59\) is not an integer)
- \(60\) (not a factor, \(70 \div 60\) is not an integer)
- \(61\) (not a factor, \(70 \div 61\) is not an integer)
- \(62\) (not a factor, \(70 \div 62\) is not an integer)
- \(63\) (not a factor, \(70 \div 63\) is not an integer)
- \(64\) (not a factor, \(70 \div 64\) is not an integer)
- \(65\) (not a factor, \(70 \div 65\) is not an integer)
- \(66\) (not a factor, \(70 \div 66\) is not an integer)
- \(67\) (not a factor, \(70 \div 67\) is not an integer)
- \(68\) (not a factor, \(70 \div 68\) is not an integer)
- \(69\) (not a factor, \(70 \div 69\) is not an integer)
- \(70\) (since \(70 \div 70 = 1\))
The factors of \(70\) are:
\[
1, 2, 5, 7, 10, 14, 35, 70
\]
### Final Answer
The number is \(70\) and its factors are \(1, 2, 5, 7, 10, 14, 35, 70\).
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