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EXERCISE 2.2

1. Which of the following numbers are divisible by 2, 3, and 6?
a. 31,290
b. 97,656
c. 987,654
d. 778,126
e. 1,790,184
f. 800,552
g. 4,883
h. 973,212

2. Which of the following numbers are divisible by 5 and 10?
a. 452,250
b. 1,255
c. 1,000
d. 100,025
e. 243



Answer :

GinnyAnswer
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

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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