Answer :
To find the remainder when [tex]\(349 \times 74 \times 36\)[/tex] is divided by 3, we can use the properties of divisibility. The key idea is to determine the remainder of each factor when divided by 3, and then use these to find the remainder of the entire product.
1. Determine Remainder of Each Number:
- 349 Divided by 3:
- Add the digits of 349: [tex]\(3 + 4 + 9 = 16\)[/tex]
- Add the digits of 16: [tex]\(1 + 6 = 7\)[/tex]
- Since 7 is not divisible by 3, the remainder is 1.
- 74 Divided by 3:
- Add the digits of 74: [tex]\(7 + 4 = 11\)[/tex]
- Add the digits of 11: [tex]\(1 + 1 = 2\)[/tex]
- Since 2 is not divisible by 3, the remainder is 2.
- 36 Divided by 3:
- Add the digits of 36: [tex]\(3 + 6 = 9\)[/tex]
- Since 9 is divisible by 3, the remainder is 0.
2. Finding the Remainder of the Product:
The remainder when a product is divided by a number can be found by multiplying the remainders of the factors.
- Multiplying the remainders: [tex]\(1 \times 2 \times 0 = 0\)[/tex]
3. Conclusion:
Therefore, the remainder when [tex]\(349 \times 74 \times 36\)[/tex] is divided by 3 is 0.
1. Determine Remainder of Each Number:
- 349 Divided by 3:
- Add the digits of 349: [tex]\(3 + 4 + 9 = 16\)[/tex]
- Add the digits of 16: [tex]\(1 + 6 = 7\)[/tex]
- Since 7 is not divisible by 3, the remainder is 1.
- 74 Divided by 3:
- Add the digits of 74: [tex]\(7 + 4 = 11\)[/tex]
- Add the digits of 11: [tex]\(1 + 1 = 2\)[/tex]
- Since 2 is not divisible by 3, the remainder is 2.
- 36 Divided by 3:
- Add the digits of 36: [tex]\(3 + 6 = 9\)[/tex]
- Since 9 is divisible by 3, the remainder is 0.
2. Finding the Remainder of the Product:
The remainder when a product is divided by a number can be found by multiplying the remainders of the factors.
- Multiplying the remainders: [tex]\(1 \times 2 \times 0 = 0\)[/tex]
3. Conclusion:
Therefore, the remainder when [tex]\(349 \times 74 \times 36\)[/tex] is divided by 3 is 0.
