prime factorization of 1078
To find the prime factorization of 1078, we divide it by its smallest prime factor, which is 2:
1078 ÷ 2 = 539
Next, we divide 539 by its smallest prime factor, which is 7:
539 ÷ 7 = 77
Lastly, we divide 77 by its smallest prime factor, which is 7:
77 ÷ 7 = 11
Therefore, the prime factorization of 1078 is 2 × 7 × 7 × 11.
To find the prime factorization of a number, you need to determine the prime numbers that, when multiplied together, give you the original number. Let's find the prime factorization of 1078:
1. Start by dividing the number by the smallest prime number, which is 2.
1078 ÷ 2 = 539
2. Since 2 is not a factor of 539, move on to the next prime number, which is 3.
539 ÷ 3 = 179.67
3. Since 3 is also not a factor of 539, move on to the next prime number, which is 5.
539 ÷ 5 = 107.8
4. Finally, divide by the next prime number, 7.
107.8 ÷ 7 = 15.4
5. We can see that 1078 is not divisible by any more prime numbers greater than 7.
To summarize, the prime factorization of 1078 is: 2 × 7 × 7 × 11 = 2 × 7² × 11.
To find the prime factorization of 1078, we can divide it by prime numbers until we cannot divide any further.
1. Start by dividing 1078 by the smallest prime number, which is 2. Since 1078 is an even number, it can be divided by 2.
1078 ÷ 2 = 539
2. Now, we repeat the process with the new quotient, which is 539. Divide it by 2 again.
539 ÷ 2 = 269.5
Since the quotient is not a whole number, we move on to the next prime number.
3. Divide 539 by the next prime number, which is 3.
539 ÷ 3 = 179.67
Again, the quotient is not a whole number, so we move on to the next prime number.
4. Divide 539 by the next prime number, which is 5.
539 ÷ 5 = 107.8
The quotient is not a whole number, so we move on to the next prime number.
5. Divide 539 by the next prime number, which is 7.
539 ÷ 7 = 77
Finally, we have obtained a whole number quotient. Now we continue with the prime factorization of 77.
6. Divide 77 by the smallest prime number, which is 2.
77 ÷ 7 = 11
Again, we have obtained a whole number quotient. Now we continue with the prime factorization of 11.
7. Divide 11 by the smallest prime number, which is 2.
11 ÷ 11 = 1
We have reached a quotient of 1, which means we have found all the prime factors.
Therefore, the prime factorization of 1078 is: 2 × 7 × 7 × 11.