Prime Factorisation

Step 1: Write (486=2\times243). Step 2: Since (243=3^5), (486=2\times3^5). Step 3: Do not leave 243 in the final answer; write it as a power of 3.

Step 1: Write (600=6\times100). Step 2: (6=2\times3) and (100=2^2\times5^2), so (600=2^3\times3\times5^2). Step 3: Be careful while counting the total power of 2.

Step 1: Write (675=27\times25). Step 2: (27=3^3) and (25=5^2), so (675=3^3\times5^2). Step 3: 27 and 25 are composite, so convert them into prime powers.

Step 1: Write (720=72\times10). Step 2: (72=2^3\times3^2) and (10=2\times5), so (720=2^4\times3^2\times5). Step 3: Break 72 completely into prime form.

Step 1: Write (756=27\times28). Step 2: (27=3^3) and (28=2^2\times7), so (756=2^2\times3^3\times7). Step 3: Convert 28 into (2^2\times7).

Step 1: Recognise (784=28^2). Step 2: Since (28=2^2\times7), (784=2^4\times7^2). Step 3: In a square number, exponents may be even, so check the powers.

Step 1: Write (840=84\times10). Step 2: (84=2^2\times3\times7) and (10=2\times5), so (840=2^3\times3\times5\times7). Step 3: Break all composite factors down to primes.

Step 1: Write (900=9\times100). Step 2: (9=3^2) and (100=2^2\times5^2), so (900=2^2\times3^2\times5^2). Step 3: 900 is a square number, so even exponents appear.

Step 1: Write (945=27\times35). Step 2: (27=3^3) and (35=5\times7), so (945=3^3\times5\times7). Step 3: Do not forget to change 27 into (3^3).

Step 1: (1000) can be written as (10^3). Step 2: Since (10=2\times5), (1000=2^3\times5^3). Step 3: 10 is composite, so write 2 and 5 in the final prime form.

Step 1: Divide 1024 repeatedly by 2. Step 2: Ten factors of 2 give (1024=2^{10}). Step 3: 4 and 32 are composite, so write the power of 2 in final prime form.

Step 1: Write (1155=11\times105). Step 2: (105=3\times5\times7), so (1155=3\times5\times7\times11). Step 3: 105 is composite, so break it further.

Step 1: Write (1176=24\times49). Step 2: (24=2^3\times3) and (49=7^2), so (1176=2^3\times3\times7^2). Step 3: Write both 24 and 49 in prime form.

Step 1: Recognise (1225=35^2). Step 2: Since (35=5\times7), (1225=5^2\times7^2). Step 3: 35 is composite, so write prime bases 5 and 7.

Step 1: Write (1296=16\times81). Step 2: (16=2^4) and (81=3^4), so (1296=2^4\times3^4). Step 3: Convert 16 and 81 into prime powers.

Step 1: Write (1323=27\times49). Step 2: (27=3^3) and (49=7^2), so (1323=3^3\times7^2). Step 3: Do not leave 27 and 49 in the final form.

Step 1: Write (1440=144\times10). Step 2: (144=2^4\times3^2) and (10=2\times5), so (1440=2^5\times3^2\times5). Step 3: The total power of 2 is 5, so count it carefully.

Step 1: Write (1575=225\times7). Step 2: (225=3^2\times5^2), so (1575=3^2\times5^2\times7). Step 3: Convert 225 into prime powers.

Step 1: Recognise (1728=12^3). Step 2: Since (12=2^2\times3), (12^3=2^6\times3^3). Step 3: 12 is composite, so write powers of 2 and 3 in the final prime form.

Step 1: (1764=42^2). Step 2: Since (42=2\times3\times7), (1764=2^2\times3^2\times7^2). Step 3: In a square number, each prime power should be even.

Step 1: Write (1800=18\times100). Step 2: (18=2\times3^2) and (100=2^2\times5^2), so (1800=2^3\times3^2\times5^2). Step 3: Break 18 and 100 separately into prime form.

Step 1: Write (2025=81\times25). Step 2: (81=3^4) and (25=5^2), so (2025=3^4\times5^2). Step 3: Convert 81 and 25 into prime powers.

Step 1: Divide 2187 repeatedly by 3. Step 2: Seven factors of 3 give (2187=3^7). Step 3: 9 and 27 are composite, so keep base 3 in the final form.

Step 1: (2401) can be written as (49\times49). Step 2: Since (49=7^2), (2401=7^4). Step 3: 49 is composite, so write the power of 7 in final prime form.

Step 1: Write (2500=25\times100). Step 2: (25=5^2) and (100=2^2\times5^2), so (2500=2^2\times5^4). Step 3: The total power of 5 is 4, so count carefully.