Answer:
There are 7 copies of 2 and 1 copy of 11 in the product:
1408 = 2^7×11
Step-by-step explanation:
Factor the following integer:
1408
The last digit of 1408 is 8, which means it is even. Therefore 1408 is divisible by 2:
1408 = 2 704:
1408 = 2×704
The last digit of 704 is 4, which means it is even. Therefore 704 is divisible by 2:
704 = 2 352:
1408 = 2×2×352
The last digit of 352 is 2, which means it is even. Therefore 352 is divisible by 2:
352 = 2 176:
1408 = 2×2×2×176
The last digit of 176 is 6, which means it is even. Therefore 176 is divisible by 2:
176 = 2 88:
1408 = 2×2×2×2×88
The last digit of 88 is 8, which means it is even. Therefore 88 is divisible by 2:
88 = 2 44:
1408 = 2×2×2×2×2×44
The last digit of 44 is 4, which means it is even. Therefore 44 is divisible by 2:
44 = 2 22:
1408 = 2×2×2×2×2×2×22
The last digit of 22 is 2, which means it is even. Therefore 22 is divisible by 2:
22 = 2 11:
1408 = 2×2×2×2×2×2×2×11
11 is not divisible by 2 since 11 is odd and 2 is even:
1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2)
The sum of the digits of 11 is 1 + 1 = 2, which is not divisible by 3. This means 11 is not divisible by 3:
1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2 or 3)
The last digit of 11 is not 5 or 0, which means 11 is not divisible by 5:
1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2, 3 or 5)
Divide 7 into 11:
| | 1 | (quotient)
7 | 1 | 1 |
- | | 7 |
| | 4 | (remainder)
11 is not divisible by 7:
1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2, 3, 5 or 7)
No primes less than 11 divide into it. Therefore 11 is prime:
1408 = 2×2×2×2×2×2×2×11
There are 7 copies of 2 and 1 copy of 11 in the product:
Answer: 1408 = 2^7×11
= 21 x 21 x 21 x 21 x 21 x 5 = 20 420 505