Divisibility Rules & Digital Root Testsविभाज्यता के नियम एवं अंक योग परीक्षण
Comprehensive guide to divisibility shortcuts, alternating sum for 11, unit digit trimming for 7 and 13, and coprimality factor tests.
Overview: Divisibility Rules & Digital Root Tests अवलोकन: विभाज्यता के नियम एवं अंक योग परीक्षण
Divisibility rules allow quick verification without manual long division:
• Divisibility by 2, 4, 8, 16: Last 1, 2, 3, or 4 digits divisible by 2, 4, 8, or 16 respectively.
• Divisibility by 3 & 9: Sum of all digits divisible by 3 or 9 respectively.
• Divisibility by 7: Double the last digit and subtract from the remaining number; result must be divisible by 7.
• Divisibility by 11: (Sum of digits at odd places) - (Sum of digits at even places) must be 0 or a multiple of 11.
• Divisibility by 13: Multiply the last digit by 4 and add to the remaining number; result must be divisible by 13.
• Composite Numbers: If a number is divisible by co-prime factors a and b, it is divisible by a × b (e.g., 72 = 8 × 9; 88 = 8 × 11; 99 = 9 × 11).
Divisibility by 2, 3, 4, 5, 7, 8, 9, 11, 13, and composite co-prime factors