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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, 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.
Step 1: Write (2268=4\times567). Step 2: (4=2^2) and (567=3^4\times7), so (2268=2^2\times3^4\times7). Step 3: Convert 567 into complete prime form.
Step 1: Write (2340=234\times10). Step 2: (234=2\times3^2\times13) and (10=2\times5), so (2340=2^2\times3^2\times5\times13). Step 3: The power of 2 becomes 2.
Step 1: Write (2450=2\times1225). Step 2: (1225=5^2\times7^2), so (2450=2\times5^2\times7^2). Step 3: Convert 1225 into prime powers.
Step 1: Write (2640=16\times165). Step 2: (16=2^4) and (165=3\times5\times11), so (2640=2^4\times3\times5\times11). Step 3: Break 165 further.
Step 1: Write (2835=81\times35). Step 2: (81=3^4) and (35=5\times7), so (2835=3^4\times5\times7). Step 3: Change 81 into (3^4).
Step 1: Write (3120=16\times195). Step 2: (16=2^4) and (195=3\times5\times13), so (3120=2^4\times3\times5\times13). Step 3: Give 195 its complete prime form.
Step 1: Write (3402=2\times1701). Step 2: (1701=3^5\times7), so (3402=2\times3^5\times7). Step 3: Convert 1701 into prime form using 3 and 7.
Step 1: Write (3528=72\times49). Step 2: (72=2^3\times3^2) and (49=7^2), so (3528=2^3\times3^2\times7^2). Step 3: Convert 72 and 49 into prime powers.
Step 1: Write (3645=729\times5). Step 2: Since (729=3^6), (3645=3^6\times5). Step 3: 729 should not be left in the final form.
Step 1: Write (3888=16\times243). Step 2: (16=2^4) and (243=3^5), so (3888=2^4\times3^5). Step 3: Change 243 into a power of 3.
Step 1: Write (3969=81\times49). Step 2: (81=3^4) and (49=7^2), so (3969=3^4\times7^2). Step 3: Write both parts as prime powers.
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: Comparing gives (a=5).
Step 1: (2205=45\times49). Step 2: (45=3^2\times5) and (49=7^2), so (2205=3^2\times5\times7^2). Step 3: Comparing gives (b=2).
Step 1: (2450=2\times1225). Step 2: (1225=5^2\times7^2), so (2450=2\times5^2\times7^2). Step 3: Comparing with the given form gives (m=2).
Step 1: Write (3888=16\times243). Step 2: (16=2^4) and (243=3^5), so the power of 2 is 4. Step 3: Comparing gives (p=4).
QUIZ COMPLETE
