DIVISIBILITY
What do we understand as divisibility?
It's the property a number has of being divided by another number in an exact number of times or with a remainder of zero.
3.1
Thus, 24 is divisible by 3.
3.2 Is 24 divisible by 2?
Yes, because the remainder is zero when you divide it by 2 and the quotient, 12.
HOW DO WE KNOW IF A NUMBER IS DIVISIBLE BY ANOTHER WITHOUT CARRYING OUT THE DIVISION?
Divisibility by 2:
A number is divisible by 2 if the number ends in ZERO or AN EVEN NUMBER:
32, 128, 400, 10, 23124…………………..ARE DIVISIBLE BY 2 because they end in zero or an even number.
Divisibility by 3:
A number is divisible by 3 when the sum of its digits equals 3 or a multiple of 3.
45, 63, 21, 675, 12348…………ARE DIVISIBLE BY 3, because if you add their digits, they equal 3 or a multiple of 3:
Since 18 divided by 3 is 6 and the remainder is zero, 675 is divisible by 3.
If you add the digits of the number 18 (1+8), you will get an answer of 9, and 9 is divisible by 3.
3.3 Which of the following numbers is divisible by 2 or by 3?:
Answers:
36, 12 and 114 are divisible by 2 and by 3 because they end in an even number and because the sum of its digits give a multiple of three.
26 is not divisible by 3 because the sum of its digits equal 8. It is divisible by 2, because it ends in an even number.
2343 is not divisible by 2 because it doesn't end in an even number or in zero. It is divisible by 3 since the sum of its digits equal 12 and this number is divisible by 3.
Divisibility by 4:
A number is divisible by 4 when the number formed by the two last digits is a multiple of 4 or the two last digits are two zeros.
3.4 400, 1024, 144, 256, 7000, 1516. Are they divisible by 4?
Yes: 400 and 7000: because they end in two zeros (or more).
Yes: 1024, 144, 256, 1516: because the two last digits of each one of them can be divided by 4 and we get a remainder of zero.
Divisibility by 5:
A number is divisible by 5 when it ends in zero or in 5.
Examples: 120,125,151005,……
Answer the following questions:
3.5 360 is divisible by which numbers?
3.6 120 is divisible by which numbers?
3.7 300 is divisible by which numbers?
3.8 363 is divisible by which numbers?
Answers:
3.5 360 is divisible by 2, because it ends in zero. 3, because the sum of its digits equal 9 and 9 is multiple of 3. 4, because the two last digits, 60, is a multiple of 4. 5, because it ends in zero.
3.6 120 is divisible by 2, 3, 4 and 5
3.7 300 is divisible by 2, 3, 4 and 5 (by 4 because it ends in two zeros).
3.8 363 is divisible by 3. The sum of its digits: 3+6+3 = 9 is a multiple of 3.
