Problems for the MIDDLE SCHOOL

TITUS, SNEHA (2017) Problems for the MIDDLE SCHOOL. At Right Angles, 6 (2). pp. 86-91.

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Abstract

Our focus this time is a step forward from parity (our theme for the last issue). In this issue, our problems are all based on multiples and factors; I’m sure you’ll enjoy verifying and proving these number facts, and playing these games which improve your understanding of factorization and the divisibility rules. The following basic rule will help you: If the prime factorization of a number N is given by N = p b 1 1 × . . . × p b k k , then the number has ( b 1 + 1 )( b 2 + 1 )( b 3 + 1 ) . . . . . . . . . . . . . . . . . . . . . ( b k + 1 ) factors. For example, 75 = 3 × 5 2 has ( 1 + 1 )( 2 + 1 ) = 6 factors, viz., 1 , 3 , 5 , 15 , 25 , 75. This is pretty easy to reason out: the factors can have no 3s or one 3, no 5s or one 5 or two 5s. So there are 2 ways in which 3 can be a factor and 3 ways in which 5 can be a factor and so 3 × 2 = 6 possible factors

Item Type: Articles in APF Magazines
Uncontrolled Keywords: Multiples, factors, divisibility, factorization, primes, place value, number of factors
Subjects: Natural Sciences
Natural Sciences > Mathematics
Divisions: Azim Premji University > University publications > At Right Angles
Depositing User: Mr. Sachin Tirlapur
Date Deposited: 15 Sep 2018 14:41
Last Modified: 15 Sep 2018 14:41
URI: http://publications.azimpremjifoundation.org/id/eprint/1376
Publisher URL: http://apfstatic.s3.ap-south-1.amazonaws.com/s3fs-...

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