 | John Hind - 1837 - 584 σελίδες
...situations. 351. In any scale of notation whose radix is r, a number N when divided by r — 1, leaves the same remainder as the sum of its digits, when divided by r — 1, leaves. For, let N = a + br + cr2 + dr3 + &c. = b(r - 1) + c(r* - 1) + d(f -l) + Sic. + a... | |
 | Robert Simson (master of Colebrooke house acad, Islington.) - 1838 - 206 σελίδες
...Divide 20 into two parts which shall be to each other as 2 to 3. Example of a theorem : Prove that any number divided by 9 will leave the same remainder as the sum of its digits or figures divided by 9. 10. The investigation or solution of a problem may either be conducted by... | |
 | George Roberts Perkins - 1841 - 274 σελίδες
...follows that the first number, 78534, will be divisible by 9 when the sum of its digits (7+8 + 5+3 + 4) is. Hence it follows, that any number being diminished...divided by 9 will leave the same remainder as the sum of the digits when divided by 9. NOTE.—These singular properties of the digit 9, have been made use... | |
 | Charles Guilford Burnham - 1841 - 324 σελίδες
...proof depends upon a property of the number 9, which belongs to no other digit but 3; — namely, that any number divided by 9 will leave the same remainder as the sum of its figures, or digits, divided by 9. EXERCISES. 237456 478145 632891 4(57892 956736 357607 736345 202379... | |
 | Charles Waterhouse - 1842 - 180 σελίδες
...figure 9 has a peculiar property, which, except 3, belongs to no other figure whatever, viz : that any number divided by 9 will leave the same remainder as the sum of its figures divided by 9. NOTE 1. — Compound Addition differs from Simple Addition only in the succession... | |
 | Alfred Crowquill - 1843 - 156 σελίδες
...property of the number 9, which, except the number 3, belongs to no other digit whatever ; namely, that " any number divided by 9, will leave the same remainder as the sum of its figures or digits divided by 9." Multiply 3542 by ' 6196 or Multiply 6196 by " 3542 21252 31878 3542... | |
 | Charles WATERHOUSE - 1844 - 228 σελίδες
...figure 9 has a peculiar property, which, except 3, belongs to no other figure whatever, viz. : that any number ^divided by 9, will leave the same remainder as the sum of its figures divided by 9. Also, any whole number of tens, hundreds, thousands, &c., contains as many nines... | |
 | James Bates Thomson - 1846 - 354 σελίδες
...consequently we divide by a prime number. (Art. 102.) 15. Any number expressed by the decimal notation, divided by 9, will leave the same remainder as the sum of its figures or digits divided by 9. The same property belongs to the number 3, and to no other number.... | |
 | James Bates Thomson - 1846 - 362 σελίδες
...consequently we divide by a prime number. (Art. 102.) 15. Any number expressed by the decimal notation, divided by 9, will leave the same remainder as the sum of its figures or digits divided by 9. The same property belongs to the number 3, and to no other number.... | |
 | James Bates Thomson - 1846 - 402 σελίδες
...consequently we divide by a prime number. (Art. 102.) 15. Any number expressed by the decimal notation, divided by 9, will leave the same remainder as the sum of its figures or digits divided by 9. The same property belongs to the number 3, and to no other number.... | |
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... any number divided by 9 will leave the same remainder as the sum of its digits divided by 9. 
