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Test of Divisibility

Test of Divisibility. a number is divisible by: 2 – if the number is even or the numeral in the ones’ place is either 0,2,4,6,8 Example: 202, 30 8 , 109 0. 3 – if the sum of the digits is a multiple of 3 Example: 4569 (4 + 5 + 6+ 9= 24 ).

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Test of Divisibility

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  1. Test of Divisibility

  2. a number is divisible by: 2 – if the number is even or the numeral in the ones’ place is either 0,2,4,6,8 Example: 202, 308, 1090

  3. 3– if the sum of the digits is a multiple of 3 Example: 4569 (4 + 5 + 6+ 9= 24 )

  4. 4– if the number formed by the last two numerals on the right is a multipe of 4 Example: 1312 (12/4 = 3 )

  5. 5– if the numeral in the ones’ place is 0 or 5 Example: 1000, 3685, 105

  6. 6– if then number is even and is also divisible by 3 Example: 114 (1 + 1 + 4 =6) Even

  7. 7– If you double the last digit and subtract it from the rest of the number and the answer is: 0, or divisible by 7 Example: 672 (Double 2 is 4, 67-4=63, and 63÷7=9) 

  8. 8– if the number formed by the last three numerals on the right is a multiple of 8 Example: 109816

  9. 9– if the sum of the digits is a multiple of 9 Example: 1629 ( 1+6+2+9=18) (1+8=9)

  10. 10 – if the numeral on the ones place is 0 Example: 100, 50, 18390

  11. The Sieve of Eratosthenes

  12. 200 B.C. – discovered a pattern of dividing the set of counting numbers except 1 into prime and composite

  13. Eratosthenes (276-196 B.C.) • Greek mathematician, astronomer, geographer • Measured the circumference of the Earth with extraordinary accuracy • Born in Cyrene (Shahhat, Libya) • Greek poet teacher- Callimachus • 240 B.C.- became the head of the library in Alexandria • Calculate by Trigonometry both the distance to the sun and the circumference of the Earth • Most important work was a systematic treatise on geography

  14. Complete Factorization

  15. Carl Friedrich Gauss (1777-1855) • German mathematician • Wide ranging contributions to Physics- the study of electromagnetism • Born in Braunschweig (April 30, 1777) • Studied ancient language but became interested in Mathematics (17 yrs. Old) • The Fundamental Theorem of Algebra

  16. Thank You

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