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SubjectsMathematics
अभाज्य गुणनखंडन
In Class 10 Mathematics, under the Real Numbers chapter, Prime Factorisation teaches students to express a composite number as a product of prime numbers. Students practise identifying prime factors and writing factorisations using multiplication and exponents. This foundational skill supports the Fundamental Theorem of Arithmetic and later work with HCF and LCM.
TOPIC PRACTICE
Up to 25 questions from this page. Select your focus, then start.
Step 1: In prime factorisation, a number is written as a product of prime numbers. Step 2: If any composite factor remains, the form is not final. Step 3: In exams, write only prime bases and their powers in the final answer.
Step 1: Write (504=8\times63). Step 2: (8=2^3) and (63=3^2\times7), so (504=2^3\times3^2\times7). Step 3: Do not leave composite forms like 8 and 63 in the final answer.
Step 1: (528) can be written as (16\times33). Step 2: (16=2^4) and (33=3\times11), so (528=2^4\times3\times11). Step 3: Since 33 is composite, split it into 3 and 11.
Step 1: Write (560=16\times35). Step 2: (16=2^4) and (35=5\times7), so (560=2^4\times5\times7). Step 3: Since 35 is composite, write 5 and 7 in the final form.
Step 1: Write (630=63\times10). Step 2: (63=3^2\times7) and (10=2\times5), so (630=2\times3^2\times5\times7). Step 3: Do not keep 9 or 35 in the final form.
Step 1: (672) can be written as (32\times21). Step 2: (32=2^5) and (21=3\times7), so (672=2^5\times3\times7). Step 3: Since 21 is composite, break it further.
Step 1: Write (700=7\times100). Step 2: (100=2^2\times5^2), so (700=2^2\times5^2\times7). Step 3: It is necessary to change 100 into prime powers.
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: Give complete prime form to both parts.
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: Write (980=98\times10). Step 2: (98=2\times7^2) and (10=2\times5), so (980=2^2\times5\times7^2). Step 3: Count the total power of 2 correctly.
Step 1: Write (1008=16\times63). Step 2: (16=2^4) and (63=3^2\times7), so (1008=2^4\times3^2\times7). Step 3: Give 63 its complete prime form.
Step 1: Write (1155=11\times105). Step 2: (105=3\times5\times7), so (1155=3\times5\times7\times11). Step 3: Since 105 is composite, 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: Convert 24 and 49 into prime powers.
Step 1: Recognise (1225=35^2). Step 2: Since (35=5\times7), (1225=5^2\times7^2). Step 3: In a square number, prime exponents may be even.
Step 1: Write (1296=16\times81). Step 2: (16=2^4) and (81=3^4), so (1296=2^4\times3^4). Step 3: Do not leave 16 and 81 in the final answer.
Step 1: Write (1323=27\times49). Step 2: (27=3^3) and (49=7^2), so (1323=3^3\times7^2). Step 3: Both 27 and 49 are composite, so write them as prime powers.
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.
Step 1: Write (1470=30\times49). Step 2: (30=2\times3\times5) and (49=7^2), so (1470=2\times3\times5\times7^2). Step 3: Write 49 as (7^2).
Step 1: Recognise (1728=12^3). Step 2: Since (12=2^2\times3), (12^3=2^6\times3^3). Step 3: Since 12 is composite, write powers of 2 and 3 in the final form.
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: Give complete prime form to both 18 and 100.
Step 1: Write (1980=198\times10). Step 2: (198=2\times3^2\times11) and (10=2\times5), so (1980=2^2\times3^2\times5\times11). Step 3: Since 2 appears twice, write (2^2).
Step 1: (840=84\times10). Step 2: (84=2^2\times3\times7) and (10=2\times5), so (840=2^3\times3\times5\times7). Step 3: Comparing gives (a=3).
Step 1: (945=27\times35). Step 2: (27=3^3) and (35=5\times7), so (945=3^3\times5\times7). Step 3: Comparing gives (b=3).
Step 1: (1225=35^2). Step 2: Since (35=5\times7), (1225=5^2\times7^2). Step 3: Comparing with the given form gives (m=2).
Step 1: Write (1800=18\times100). Step 2: (18=2\times3^2) and (100=2^2\times5^2), so the total power of 2 is 3. Step 3: Therefore, (p=3).
QUIZ COMPLETE
