Criteria for divisibility

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Criteria for divisibility

1. 1. Criteria for Divisibility Richie O’Connor
2. 2. Criteria for Divisibility • The criteria for divisibility are practical rules (normas) which try to discover if a number is divisible by 2, 3, 4, 5, 6, 9, 10, 11 etc. • Here are the rules:
3. 3. To find out if a number is a multiple of 2 • All multiples of 2 end in either 0 – 2 – 4 – 6 – 8 • For example: • 2 4 6 8 10 • 12 14 16 18 20 • 22 24 26 28 30 • So, a number is a multiple of 2 if the number ends in: • 0 – 2 – 4 – 6 – 8.
4. 4. To find out if a number is a multiple of 3 • Take any multiple of 3 and add the figures in the number. • You will see that the sum of the figures is a multiple of 3. • For example: • 3 · 11 = 33 → 3 + 3 = 63 · 11 = 33 → 3 + 3 = 6 →→ 6 is a multiple of 36 is a multiple of 3 • 3 · 24 = 72 → 7 + 2 = 93 · 24 = 72 → 7 + 2 = 9 →→ 9 is a multiple of 39 is a multiple of 3 • 3 · 136 = 408 → 4 + 0 + 8 = 12 →3 · 136 = 408 → 4 + 0 + 8 = 12 → 12 is a multiple of 312 is a multiple of 3 • So, a number is a multiple of 3 if the sum of its figures is a multiple of 3
5. 5. To find out if a number is a multiple of 4 • A number is a multiple of 4 if the two last figures are 00 or multiples of 4. • For example: • 140 → -40 = 2 last figures → 140 is a multiple of 4 • 256 → -56 = 2 last figures → 256 is a multiple of 4 • 1,664 → -64 = 2 last figures → 1,664 is a multiple of 4 • 1,500 → -00 = 2 last figures → 1,500 is a multiple of 4 • So, if the two last figures are -00 or a multiple of 4, the number is a multiple of 4.
6. 6. To find out if a number is a multiple of 5 • All the multiples of 5 end in either 0 or 5. • For example: • 5 10 • 15 20 • 25 30 • So, a number is a multiple of 5 if the last number is 0 or 5
7. 7. To find out if a number is a multiple of 6 • A number is a multiple of 6 is you can divide by 2 and 3 at the same time. • For example: • 24 → you can divide by 2 and 3 at the same time • 366 → you can divide by 2 and 3 at the same time • 2,382 → you can divide by 2 and 3 at the same time • So, if you can divide by 2 and 3 at the same time, the number is a multiple of 6
8. 8. To find if a number is a multiple of 9 • A number is a multiple of 9 if the sum of its figures is a multiple of 9 • For example: • 333 → 3 + 3 + 3 = 9 → 333 is a multiple of 9 • 1,242 → 1 + 2 + 4 + 2 = 9 → 1,242 is a multiple of 9 • 5,670 → 5 + 6 + 7 + 0 = 18 → 5,670 is a multiple of 9 • 9,837 → 9 + 8 + 3 + 7 = 27 → 9,837 is a multiple of 9 • So, if the sum of its figures is a multiple of 9, the number is a multiple of 9.
9. 9. To find if a number is a multiple of 10 • If the number finishes in -0 (zero) it is a multiple of 10. • For example: • 10 20 • 30 40 • 50 60 • So, if a number finishes in -0 (zero) it is a multiple of 10.
10. 10. To find out if a number is a multiple of 11 • You can divide a number by 11 if you add the figures which are in even positions and then add the figures in odd positions. • If you subtract the numbers and the result is 0 or a multiple of 11, then the number is a multiple of 11. • For example: • the number 74,921 can be divided by 11. • Sum of the figures in even positions: 4 + 2 = 6 • Sum of the figures in odd positions: 7 + 9 + 1 = 17 • We subtract them: 17 – 6 = 11 → 11 is a multiple of 11, so the number is a multiple of 11.
11. 11. Prime Numbers and Composite Numbers
12. 12. Prime Numbers • Prime numbers are numbers that can only be divided by 1 and the number itself. • For example: • 7 • Divide by 1? Yes • Divide by 2? No • Divide by 3? No • Divide by 4? No • Divide by 5? No • Divide by 6? No • Divide by 7? Yes • So, 7 is a prime number
13. 13. Composite Numbers • All other numbers are composite numbers. • They are numbers with divisors other than 1 and the number itself. • For example: • 6 • Divide by 1? Yes • Divide by 2? Yes • Divide by 3? Yes • Divide by 4? No • Divide by 5? No • Divide by 6? Yes • So, the divisors of 6 are 1, 2, 3, 6 → it is a composite number.