16
Divisibility rule for 3
Textbook: Part 1, lesson 16, pp. 49–51
GoalKnow and use the divisibility rule for 3.
New words
sum of digits · raqamlar yig‘indisimultiple of 3 · 3 ga karralidivisibility rule · bo‘linish alomatiremainder · qoldiq
Explanation
Divisibility rule for 3: if the sum of the digits of a number is divisible by 3, the number is divisible by 3. For example, in 2 148 we get 2 + 1 + 4 + 8 = 15, and 15 divides by 3, so 2 148 divides by 3. In 4 721 we get 4 + 7 + 2 + 1 = 14, which does not divide by 3, so 4 721 does not either.
Worked examples
2 148: 2 + 1 + 4 + 8 = 15 and 15 : 3 = 5, so the number is divisible by 3.
4 721: 4 + 7 + 2 + 1 = 14, which is not divisible by 3, so the number is not divisible by 3.
Class activity
“Digit sums”: each pair writes a three-digit number, finds its digit sum and predicts whether it divides by 3; then they divide to check.
Practice
1
What is the sum of the digits of 7 305?
15
2
From 27, 34, 51, 62, 78, 85, 93, 100 write those divisible by 3.
27, 51, 78, 93
3
Which digits can replace the star so that 41* is divisible by 3?
1, 4 or 7
4
534 walnuts were shared equally into 3 bags. How many walnuts are in each bag?
178