Introduction of exponents to write prime factors:
In mathematics a number or an expression can be factored. A number can be factored only by prime numbers or by a non – prime number or by a combination of prime numbers and a non prime number. A prime number is a number which should divide by itself or by 1. When factorization of a number takes place it is written as exponents finally. Prime factoring is done from the smallest prime and goes upwards.
Exponents to Write Prime Factors Example 1
Write the number 10000 in prime numbers with exponents.
Solution: Given 10000,
Let’s start from the lowest prime 2.
10000 can be written as 2 * 5000.
Now take 5000 and write it in prime factors
5000 is same as 2 * 2500
Take 2500 and write it in prime factors.
2500 is equal to 2 *1250.
Take 1250 and write it in prime factors.
2* 625.
Now take 625 which cannot be factor with 2.
So, take the next prime 3, which is also not possible.
Now take next prime 5 and write 625 in factor form with 5
625 = 5 * 125.
Take 125 and prime factor it now and start from the lowest prime
125 = 5 * 25
Take 25 which is 5 * 5
Take 5 which is 5 * 1.
So the prime factors of 10000 is
=10000
=2 * 5000
=2 * 2 * 2500
=2 * 2 * 2 *1250
=2 * 2 * 2 * 625
=2 * 2 * 2 * 5 * 125
=2 * 2 * 2 * 5 * 5 * 25
=2 * 2 * 2 *5 * 5 * 5 * 5
=23*54, which is the exponents to write prime factors.
Between, if you have problem on these topics find the prime factorization of 125, please browse expert math related websites for more help on prime factorization word problems.
Exponents to Write Prime Factors Example 2 and 3
Write the number 75 in prime numbers with exponents.
Solution: Given 75,
To factor using prime numbers take the least prime 2 first which is not possible.
So take the next prime 3 and write the 75 in terms of 3
75 = 3 * 25.
Now factor the 25 with the prime numbers.
25 cannot be factor in terms of 3. So take the next prime number 5 and write 25 in terms of 5
25 = 5 * 5
=75
=3 * 25
=3* 5 * 5
=31 * 52, which is the exponents to write prime factors.
Write the number 175 in prime number with exponents.
Solution: Given 175,
175 can be written as 5 * 35
Now factor 35 with prime numbers.
35 can be written as 5 * 7
7 can be factor as 7* 1
=35
=5 * 35
=5 * 5 * 7
=5 * 5 * 7 *1
=52 * 71
Which is the exponents to write prime factors.
In mathematics a number or an expression can be factored. A number can be factored only by prime numbers or by a non – prime number or by a combination of prime numbers and a non prime number. A prime number is a number which should divide by itself or by 1. When factorization of a number takes place it is written as exponents finally. Prime factoring is done from the smallest prime and goes upwards.
Exponents to Write Prime Factors Example 1
Write the number 10000 in prime numbers with exponents.
Solution: Given 10000,
Let’s start from the lowest prime 2.
10000 can be written as 2 * 5000.
Now take 5000 and write it in prime factors
5000 is same as 2 * 2500
Take 2500 and write it in prime factors.
2500 is equal to 2 *1250.
Take 1250 and write it in prime factors.
2* 625.
Now take 625 which cannot be factor with 2.
So, take the next prime 3, which is also not possible.
Now take next prime 5 and write 625 in factor form with 5
625 = 5 * 125.
Take 125 and prime factor it now and start from the lowest prime
125 = 5 * 25
Take 25 which is 5 * 5
Take 5 which is 5 * 1.
So the prime factors of 10000 is
=10000
=2 * 5000
=2 * 2 * 2500
=2 * 2 * 2 *1250
=2 * 2 * 2 * 625
=2 * 2 * 2 * 5 * 125
=2 * 2 * 2 * 5 * 5 * 25
=2 * 2 * 2 *5 * 5 * 5 * 5
=23*54, which is the exponents to write prime factors.
Between, if you have problem on these topics find the prime factorization of 125, please browse expert math related websites for more help on prime factorization word problems.
Exponents to Write Prime Factors Example 2 and 3
Write the number 75 in prime numbers with exponents.
Solution: Given 75,
To factor using prime numbers take the least prime 2 first which is not possible.
So take the next prime 3 and write the 75 in terms of 3
75 = 3 * 25.
Now factor the 25 with the prime numbers.
25 cannot be factor in terms of 3. So take the next prime number 5 and write 25 in terms of 5
25 = 5 * 5
=75
=3 * 25
=3* 5 * 5
=31 * 52, which is the exponents to write prime factors.
Write the number 175 in prime number with exponents.
Solution: Given 175,
175 can be written as 5 * 35
Now factor 35 with prime numbers.
35 can be written as 5 * 7
7 can be factor as 7* 1
=35
=5 * 35
=5 * 5 * 7
=5 * 5 * 7 *1
=52 * 71
Which is the exponents to write prime factors.
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