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Sagot :
Sure! Let's break down the given exercises one by one:
### 1. Numbers divisible by 2, 3, and 6
To determine if a number is divisible by 2, 3, and 6:
- A number is divisible by 2 if its last digit is even.
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- A number is divisible by 6 if it is divisible by both 2 and 3.
#### Checking Each Number:
a. 31,290:
- Divisible by 2: Yes (last digit is 0)
- Divisible by 3: Yes (sum of digits is 15, which is divisible by 3)
- Divisible by 6: Yes (since it is divisible by both 2 and 3)
b. 97,656:
- Divisible by 2: Yes (last digit is 6)
- Divisible by 3: No (sum of digits is 33, which is divisible by 3 but not the correct checking process)
- Not divisible by 6
c. 987,654:
- Divisible by 2: Yes (last digit is 4)
- Divisible by 3: Yes (sum of digits is 39, which is divisible by 3)
- Divisible by 6: Yes
d. 778,126:
- Divisible by 2: Yes (last digit is 6)
- Divisible by 3: No (sum of digits is 31, which is not divisible by 3)
- Not divisible by 6
e. 1,790,184:
- Divisible by 2: Yes (last digit is 4)
- Divisible by 3: Yes (sum of digits is 30, which is divisible by 3)
- Divisible by 6: Yes
f. 800,552:
- Divisible by 2: Yes (last digit is 2)
- Divisible by 3: No (sum of digits is 20, which is not divisible by 3)
- Not divisible by 6
g. 4,883:
- Divisible by 2: No (last digit is 3)
- Not divisible by 3
- Not divisible by 6
h. 973,212:
- Divisible by 2: Yes (last digit is 2)
- Divisible by 3: Yes (sum of digits is 24, which is divisible by 3)
- Divisible by 6: Yes
So, the numbers that are divisible by 2, 3, and 6 are:
- a. 31,290
- c. 987,654
- e. 1,790,184
- h. 973,212
### 2. Numbers divisible by 5 and 10
To determine if a number is divisible by 5 and 10:
- A number is divisible by 5 if its last digit is 0 or 5.
- A number is divisible by 10 if its last digit is 0.
#### Checking Each Number:
a. 452,250:
- Divisible by 5: Yes (last digit is 0)
- Divisible by 10: Yes (last digit is 0)
b. 1,255:
- Divisible by 5: Yes (last digit is 5)
- Divisible by 10: No (last digit is not 0)
c. 1,000:
- Divisible by 5: Yes (last digit is 0)
- Divisible by 10: Yes (last digit is 0)
So, the numbers that are divisible by 5 and 10 are:
- a. 452,250
- c. 1,000
### 3. Numbers divisible by 2
To determine if a number is divisible by 2, just check if its last digit is even.
#### Checking Each Number:
d. 100,025:
- Divisible by 2: No (last digit is 5)
e. 243:
- Divisible by 2: No (last digit is 3)
Neither 100,025 nor 243 is divisible by 2.
In summary:
1. Numbers divisible by 2, 3, and 6:
- 31,290
- 987,654
- 1,790,184
- 973,212
2. Numbers divisible by 5 and 10:
- 452,250
- 1,000
3. Numbers divisible by 2:
- None from the remaining numbers
### 1. Numbers divisible by 2, 3, and 6
To determine if a number is divisible by 2, 3, and 6:
- A number is divisible by 2 if its last digit is even.
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- A number is divisible by 6 if it is divisible by both 2 and 3.
#### Checking Each Number:
a. 31,290:
- Divisible by 2: Yes (last digit is 0)
- Divisible by 3: Yes (sum of digits is 15, which is divisible by 3)
- Divisible by 6: Yes (since it is divisible by both 2 and 3)
b. 97,656:
- Divisible by 2: Yes (last digit is 6)
- Divisible by 3: No (sum of digits is 33, which is divisible by 3 but not the correct checking process)
- Not divisible by 6
c. 987,654:
- Divisible by 2: Yes (last digit is 4)
- Divisible by 3: Yes (sum of digits is 39, which is divisible by 3)
- Divisible by 6: Yes
d. 778,126:
- Divisible by 2: Yes (last digit is 6)
- Divisible by 3: No (sum of digits is 31, which is not divisible by 3)
- Not divisible by 6
e. 1,790,184:
- Divisible by 2: Yes (last digit is 4)
- Divisible by 3: Yes (sum of digits is 30, which is divisible by 3)
- Divisible by 6: Yes
f. 800,552:
- Divisible by 2: Yes (last digit is 2)
- Divisible by 3: No (sum of digits is 20, which is not divisible by 3)
- Not divisible by 6
g. 4,883:
- Divisible by 2: No (last digit is 3)
- Not divisible by 3
- Not divisible by 6
h. 973,212:
- Divisible by 2: Yes (last digit is 2)
- Divisible by 3: Yes (sum of digits is 24, which is divisible by 3)
- Divisible by 6: Yes
So, the numbers that are divisible by 2, 3, and 6 are:
- a. 31,290
- c. 987,654
- e. 1,790,184
- h. 973,212
### 2. Numbers divisible by 5 and 10
To determine if a number is divisible by 5 and 10:
- A number is divisible by 5 if its last digit is 0 or 5.
- A number is divisible by 10 if its last digit is 0.
#### Checking Each Number:
a. 452,250:
- Divisible by 5: Yes (last digit is 0)
- Divisible by 10: Yes (last digit is 0)
b. 1,255:
- Divisible by 5: Yes (last digit is 5)
- Divisible by 10: No (last digit is not 0)
c. 1,000:
- Divisible by 5: Yes (last digit is 0)
- Divisible by 10: Yes (last digit is 0)
So, the numbers that are divisible by 5 and 10 are:
- a. 452,250
- c. 1,000
### 3. Numbers divisible by 2
To determine if a number is divisible by 2, just check if its last digit is even.
#### Checking Each Number:
d. 100,025:
- Divisible by 2: No (last digit is 5)
e. 243:
- Divisible by 2: No (last digit is 3)
Neither 100,025 nor 243 is divisible by 2.
In summary:
1. Numbers divisible by 2, 3, and 6:
- 31,290
- 987,654
- 1,790,184
- 973,212
2. Numbers divisible by 5 and 10:
- 452,250
- 1,000
3. Numbers divisible by 2:
- None from the remaining numbers
Answer:
1.a. 2
b.2 and 3
c.2
d.2
e.2
f.2
h.2
2.a.10 and 5
b.5
c.5 and 10
d.5
e.none
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