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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 the final prime factorisation, bases must be prime. Step 2: (18=2\times3^2), so (18^2) must be changed into (2^2\times3^4). Step 3: Do not leave a composite base in the final answer.
Step 1: Write (2376=8\times297). Step 2: (8=2^3) and (297=3^3\times11), so (2376=2^3\times3^3\times11). Step 3: Do not leave 297 in the final form.
Step 1: Write (3465=9\times385). Step 2: (9=3^2) and (385=5\times7\times11), so (3465=3^2\times5\times7\times11). Step 3: Give 385 its complete prime form too.
Step 1: Write (4410=90\times49). Step 2: (90=2\times3^2\times5) and (49=7^2), so (4410=2\times3^2\times5\times7^2). Step 3: Give prime form to both 90 and 49.
Step 1: Write (5040=16\times315). Step 2: (16=2^4) and (315=3^2\times5\times7), so (5040=2^4\times3^2\times5\times7). Step 3: Give 315 its complete prime form.
Step 1: Write (5292=4\times1323). Step 2: (4=2^2) and (1323=3^3\times7^2), so (5292=2^2\times3^3\times7^2). Step 3: Convert 1323 into powers of 3 and 7.
Step 1: Write (5670=81\times70). Step 2: (81=3^4) and (70=2\times5\times7), so (5670=2\times3^4\times5\times7). Step 3: It is necessary to change 81 into (3^4).
Step 1: Write (7350=150\times49). Step 2: (150=2\times3\times5^2) and (49=7^2), so (7350=2\times3\times5^2\times7^2). Step 3: Break 150 and 49 completely and separately.
Step 1: Write (7560=8\times945). Step 2: (8=2^3) and (945=3^3\times5\times7), so (7560=2^3\times3^3\times5\times7). Step 3: Do not leave 945 in the final form.
Step 1: Write (8085=15\times539). Step 2: (15=3\times5) and (539=7^2\times11), so (8085=3\times5\times7^2\times11). Step 3: Give 539 its complete prime form too.
Step 1: Write (8820=180\times49). Step 2: (180=2^2\times3^2\times5) and (49=7^2), so (8820=2^2\times3^2\times5\times7^2). Step 3: Convert 180 and 49 into prime powers.
Step 1: Write (9800=8\times1225). Step 2: (8=2^3) and (1225=5^2\times7^2), so (9800=2^3\times5^2\times7^2). Step 3: Do not leave 1225 in the final form.
Step 1: Write (10368=128\times81). Step 2: (128=2^7) and (81=3^4), so (10368=2^7\times3^4). Step 3: Write both 128 and 81 as prime powers.
Step 1: Write (12320=32\times385). Step 2: (32=2^5) and (385=5\times7\times11), so (12320=2^5\times5\times7\times11). Step 3: Give 385 its complete prime form.
Step 1: Write (13230=270\times49). Step 2: (270=2\times3^3\times5) and (49=7^2), so (13230=2\times3^3\times5\times7^2). Step 3: Do not keep 270 and 49 in the final form.
Step 1: Write (14700=300\times49). Step 2: (300=2^2\times3\times5^2) and (49=7^2), so (14700=2^2\times3\times5^2\times7^2). Step 3: Convert 300 into prime powers.
Step 1: Write (15840=32\times495). Step 2: (32=2^5) and (495=3^2\times5\times11), so (15840=2^5\times3^2\times5\times11). Step 3: Give 495 its complete prime form.
Step 1: Write (17640=8\times2205). Step 2: (2205=3^2\times5\times7^2), so (17640=2^3\times3^2\times5\times7^2). Step 3: Give 2205 its complete prime form.
Step 1: Write (20736=256\times81). Step 2: (256=2^8) and (81=3^4), so (20736=2^8\times3^4). Step 3: Convert 256 and 81 into prime powers.
Step 1: Write (22050=450\times49). Step 2: (450=2\times3^2\times5^2) and (49=7^2), so (22050=2\times3^2\times5^2\times7^2). Step 3: Give 450 its complete prime form.
Step 1: Write (27720=8\times3465). Step 2: (3465=3^2\times5\times7\times11), so (27720=2^3\times3^2\times5\times7\times11). Step 3: Give 3465 its complete prime form.
Step 1: (15840=32\times495). Step 2: (32=2^5) and (495=3^2\times5\times11), so the power of 2 is 5. Step 3: Comparing gives (a=5).
Step 1: Write (22050=450\times49). Step 2: (450=2\times3^2\times5^2) and (49=7^2), so the power of 3 is 2. Step 3: Comparing with the given form gives (b=2).
Step 1: (20736) can be written as (256\times81). Step 2: (256=2^8) and (81=3^4), so (20736=2^8\times3^4). Step 3: Comparing gives (m=8).
Step 1: For distinct prime factors, exponents are not added. Step 2: The bases are 2, 3, 5, 7, and 11. Step 3: Therefore, there are 5 distinct prime factors.
QUIZ COMPLETE
