Math / Numbers & Operations

Question16. (a) Express 10500 in term of its prime factors

Studdy Solution

STEP 1

1. We need to express the number $10500$ as a product of its prime factors.
2. Prime factorization involves breaking down a number into its basic prime number components.

STEP 2

1. Identify the smallest prime number that divides $10500$ .
2. Divide $10500$ by this prime number and continue the process with the quotient.
3. Repeat until the quotient is 1.
4. Express the original number as a product of all the prime factors obtained.

STEP 3

Identify the smallest prime number that divides $10500$ . The smallest prime number is $2$ .

STEP 4

Divide $10500$ by $2$ .
$10500 \div 2 = 5250$

STEP 5

Continue dividing by $2$ since $5250$ is even.
$5250 \div 2 = 2625$

STEP 6

Identify the next smallest prime number that divides $2625$ . The next smallest prime number is $3$ .
$2625 \div 3 = 875$

STEP 7

Identify the next smallest prime number that divides $875$ . The next smallest prime number is $5$ .
$875 \div 5 = 175$

STEP 8

Continue dividing by $5$ since $175$ is divisible by $5$ .
$175 \div 5 = 35$

STEP 9

Continue dividing by $5$ since $35$ is divisible by $5$ .
$35 \div 5 = 7$

STEP 10

The number $7$ is a prime number.

STEP 11

Express $10500$ as a product of its prime factors:
$10500 = 2^2 \times 3 \times 5^3 \times 7$
The prime factorization of $10500$ is:
$\boxed{2^2 \times 3 \times 5^3 \times 7}$

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