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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: For example, 12 can be written as (2^2\times3). Step 3: Keep only prime numbers in the final form.
Step 1: Divide 12 by 2 to get 6. Step 2: (6=2\times3), so (12=2^2\times3). Step 3: 4 and 6 are composite, so do not keep them in the final answer.
Step 1: Write 18 as (2\times9). Step 2: Since (9=3^2), (18=2\times3^2). Step 3: Do not leave 9 in the final prime form.
Step 1: Write (20=4\times5). Step 2: Since (4=2^2), (20=2^2\times5). Step 3: 4 is composite, so write (2^2) in the final form.
Step 1: Divide 24 repeatedly by 2. Step 2: (24=2\times2\times2\times3=2^3\times3). Step 3: 8 and 6 are composite, so they are not the correct prime form.
Step 1: Write (28=4\times7). Step 2: Since (4=2^2), (28=2^2\times7). Step 3: In the final answer, write (2^2) instead of 4.
Step 1: 30 can be written as (3\times10). Step 2: (10=2\times5), so (30=2\times3\times5). Step 3: Do not keep 6, 10, or 15 in the final prime form.
Step 1: Write (36=4\times9). Step 2: (4=2^2) and (9=3^2), so (36=2^2\times3^2). Step 3: In complete prime form, keep only prime bases.
Step 1: Write (42=6\times7). Step 2: (6=2\times3), so (42=2\times3\times7). Step 3: 6 is composite, so do not keep it in the final answer.
Step 1: Write (45=9\times5). Step 2: Since (9=3^2), (45=3^2\times5). Step 3: 9 is composite, so write (3^2) in the final form.
Step 1: Divide 48 repeatedly by 2. Step 2: We get (48=2^4\times3). Step 3: 16 and 6 are composite, so they are not final prime answers.
Step 1: Write (50=2\times25). Step 2: Since (25=5^2), (50=2\times5^2). Step 3: 25 is composite, so write (5^2) in the final form.
Step 1: Write (56=8\times7). Step 2: Since (8=2^3), (56=2^3\times7). Step 3: 8 is composite, so write (2^3) in the final answer.
Step 1: Write (60=6\times10). Step 2: (6=2\times3) and (10=2\times5), so (60=2^2\times3\times5). Step 3: 6 and 10 are not final prime forms.
Step 1: Write (63=9\times7). Step 2: Since (9=3^2), (63=3^2\times7). Step 3: 9 or 21 are composite, so they will not remain in the final answer.
Step 1: Write (72=8\times9). Step 2: (8=2^3) and (9=3^2), so (72=2^3\times3^2). Step 3: In prime factorisation, break 8 and 9 into prime powers.
Step 1: Write (75=3\times25). Step 2: Since (25=5^2), (75=3\times5^2). Step 3: 25 is composite, so write (5^2) in the final form.
Step 1: Write (84=4\times21). Step 2: (4=2^2) and (21=3\times7), so (84=2^2\times3\times7). Step 3: Do not keep 4 and 21 in the final answer.
Step 1: Write (90=9\times10). Step 2: (9=3^2) and (10=2\times5), so (90=2\times3^2\times5). Step 3: Write powers carefully because 3 appears twice.
Step 1: Divide 96 repeatedly by 2. Step 2: We get (96=2^5\times3). Step 3: 32 means (2^5), but in final prime form write base 2.
Step 1: Write (100=4\times25). Step 2: (4=2^2) and (25=5^2), so (100=2^2\times5^2). Step 3: Convert 4 and 25 into prime powers.
Step 1: Write (108=4\times27). Step 2: (4=2^2) and (27=3^3), so (108=2^2\times3^3). Step 3: Do not forget to change 27 into (3^3).
Step 1: Write (120=12\times10). Step 2: (12=2^2\times3) and (10=2\times5), so (120=2^3\times3\times5). Step 3: Count the total number of 2s carefully.
Step 1: Divide 125 by 5 to get 25. Step 2: (25=5^2), so (125=5^3). Step 3: 25 is composite, so the final form is (5^3).
Step 1: Write (144=16\times9). Step 2: (16=2^4) and (9=3^2), so (144=2^4\times3^2). Step 3: Perfect square numbers can have even exponents, so check the powers.
QUIZ COMPLETE
