Conditions of Digit in The Places of Positive Integers Divisible by 7

Main Article Content

Thanatyod Jampawai


We study conditions of digit in the places of positive integers divisible by gif.latex?7 . We found that the sum of products of digit in the ones place, tens place, hundreds place, thousands place, ten thousands place, hundred thousands place, millions place, ten millions place, hundred millions place, billions place, ten billions place, hundred billions place, gif.latex?\ldots  and gif.latex?1,3,2,-1,-3,-2,1,3,2,-1,-3,-2,\ldots,  respectively, is divisible by gif.latex?7. In addition, we study conditions of positive integers with same digits which are divisible by gif.latex?7.



Download data is not yet available.

Article Details

How to Cite
Jampawai ธ. (2021). Conditions of Digit in The Places of Positive Integers Divisible by 7. Mathematical Journal, 66(705), 52–64. Retrieved from
Research Article


อัจฉรา หาญชูวงศ์. (2542). ทฤษฎีจำนวน. กรุงเทพมหานคร: โรงพิมพ์แห่งจุฬาลงกรณ์-มหาวิทยาลัย.

Harnchoowong, A. (1999). Theory of Numbers. Bangkok: Chulalongkorn University Printing House.

Konick, J.-M. D. and Mercier, A. (2007). 1001 Problems in Classical Number Theory. Providence, Rhode Island: American Mathematical Society.

Nahir, Y. (2003). Tests of divisibility. International Journal for Mathematics Education in Science and Technology, 34, p. 581 - 591.

Nahir, Y. (2008). On Divisibility Tests and The Curriculum Dilemma. Sutra: International Journal of Mathematical Science Education, 1 (1), p. 16 - 29.

Niven, I., Zuherman, H. S. and Montgomery, H. L. (1991). An Introduction to The Theory of Numbers (5th ed.). New York: John Wiley & Sons, Inc.