Prime Factorisation

Step 1: Calculate (2^4=16) and (3^2=9). Step 2: (16\times9\times11=1584). Step 3: Solve powers first and then multiply.

Step 1: Calculate (2^2=4) and (3^3=27). Step 2: (4\times27\times11=1188). Step 3: Finding the value of powers first is the right method.

Step 1: Calculate (3^3=27) and (5^2=25). Step 2: (2\times27\times25=1350). Step 3: Simplifying the two powers first makes multiplication easy.

Step 1: Calculate (2^2=4) and (3^2=9). Step 2: (4\times9\times7\times11=2772). Step 3: Move step by step while multiplying.

Step 1: Write (4200=42\times100). Step 2: (42=2\times3\times7) and (100=2^2\times5^2), so (4200=2^3\times3\times5^2\times7). Step 3: Count the powers of 2 and 5 carefully.

Step 1: Write (4620=42\times110). Step 2: (42=2\times3\times7) and (110=2\times5\times11), so (4620=2^2\times3\times5\times7\times11). Step 3: Since 2 appears twice, write (2^2).

Step 1: Write (5400=54\times100). Step 2: (54=2\times3^3) and (100=2^2\times5^2), so (5400=2^3\times3^3\times5^2). Step 3: Break both 54 and 100 completely.

Step 1: Calculate (2^2=4). Step 2: (4\times3\times5\times7\times11=4620). Step 3: When there are many factors, multiply in pairs.

Step 1: Divide 8192 repeatedly by 2. Step 2: Thirteen factors of 2 give (8192=2^{13}). Step 3: 64 and 16 are composite, so write the power of 2 in final prime form.

Step 1: In prime factorisation, every final factor must be prime. Step 2: (18=2\times3^2) and (100=2^2\times5^2), so both are composite. Step 3: (18\times100) must be changed further into (2^3\times3^2\times5^2).

Step 1: In prime factorisation, identify the bases first. Step 2: Powers of the same base are compared, such as power of 2 with power of 2 and power of 3 with power of 3. Step 3: In exams, do not compare powers directly when bases are different.

Step 1: Write (1170=117\times10). Step 2: (117=3^2\times13) and (10=2\times5), so (1170=2\times3^2\times5\times13). Step 3: Do not keep 117 and 10 in the final form.

Step 1: Write (1215=243\times5). Step 2: Since (243=3^5), (1215=3^5\times5). Step 3: 243 is composite, so write it as a power of 3 in final prime form.

Step 1: Write (1344=64\times21). Step 2: (64=2^6) and (21=3\times7), so (1344=2^6\times3\times7). Step 3: Since 21 is composite, split it into 3 and 7.

Step 1: Write (1485=135\times11). Step 2: (135=3^3\times5), so (1485=3^3\times5\times11). Step 3: Give 135 its complete prime form.

Step 1: Write (1620=162\times10). Step 2: (162=2\times3^4) and (10=2\times5), so (1620=2^2\times3^4\times5). Step 3: Count the total power of 2 correctly.

Step 1: Write (1848=8\times231). Step 2: (8=2^3) and (231=3\times7\times11), so (1848=2^3\times3\times7\times11). Step 3: Give 231 its complete prime form.

Step 1: Write (1875=3\times625). Step 2: Since (625=5^4), (1875=3\times5^4). Step 3: Do not leave 625 in the final form; write (5^4).

Step 1: Write (2016=32\times63). Step 2: (32=2^5) and (63=3^2\times7), so (2016=2^5\times3^2\times7). Step 3: Convert 63 into prime powers.

Step 1: Write (2205=45\times49). Step 2: (45=3^2\times5) and (49=7^2), so (2205=3^2\times5\times7^2). Step 3: Give complete prime form to 45 and 49.