The composite number 50 lies between {blank} and {blank}, both prime numbers.
Finish the blanks
The composite number 50 lies between 47 and 53, both prime numbers.
Express the prime factorization of 1,200 as a product of prime numbers with exponents.(2 points)
{BLANK}⁴ ⋅ {BLANK} ⋅ {BLANK} ² = 1,200
2⁴ ⋅ 3 ⋅ 5² = 1,200
Jazmyn has some strips of cloth she found for her project. The widths of the different strips are 72 cm, 96 cm, and 128 cm. They are to be cut into smaller pieces. Determine the greatest possible width of each piece so that they are all the same width.(1 point) Responses 4 cm 4 cm 8 cm 8 cm 16 cm 16 cm 32 cm
To find the greatest possible width of each piece, we need to find the greatest common divisor (GCD) of the given widths.
Using the GCD method, the factors of the widths are:
- 72: 2² ⋅ 3²
- 96: 2⁵ ⋅ 3
- 128: 2⁷
Taking the highest power of each common factor, we have:
2² ⋅ 3 ⋅ 2² = 2⁴ ⋅ 3 = 16 ⋅ 3 = 48 cm
Therefore, the greatest possible width of each piece is 48 cm.
Jazmyn has some strips of cloth she found for her project. The widths of the different strips are 72 cm, 96 cm, and 128 cm. They are to be cut into smaller pieces. Determine the greatest possible width of each piece so that they are all the same width.(1 point) Responses 4 cm 8 cm 16 cm 32 cm
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