What is 41/21*45/23*49/25*53/27 ?

The solution to 41/21*45/23*49/25*53/27 is 14 721/1035

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Popular >

41/2145/2349/25*53/27

Solution

41/21 \cdot 45/23 \cdot 49/25 \cdot 53/27

Solution

14 \frac{721}{1035}

Solution steps

41/21 \cdot 45/23 \cdot 49/25 \cdot 53/27

Follow the PEMDAS order of operations

Multiply and divide (left to right)

41/21 = \frac{41}{21}

= \frac{41}{21} \cdot 45/23 \cdot 49/25 \cdot 53/27

\frac{41}{21} \cdot 45 = \frac{615}{7}

\frac{41}{21} \cdot 45

Convert element to fraction:

45 = \frac{45}{1}

= \frac{41}{21} \cdot \frac{45}{1}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{41 \cdot 45}{21 \cdot 1}

Cancel

\frac{41 \cdot 45}{21 \cdot 1} : \frac{615}{7}

\frac{41 \cdot 45}{21 \cdot 1}

Multiply the numbers:

21 \cdot 1 = 21

= \frac{41 \cdot 45}{21}

Factor the number:

45 = 3 \cdot 15

= \frac{41 \cdot 3 \cdot 15}{21}

Factor the number:

21 = 3 \cdot 7

= \frac{41 \cdot 3 \cdot 15}{3 \cdot 7}

Cancel the common factor:

3

= \frac{41 \cdot 15}{7}

Multiply the numbers:

41 \cdot 15 = 615

= \frac{615}{7}

= \frac{615}{7}

= \frac{615}{7} /23 \cdot 49/25 \cdot 53/27

\frac{615}{7} /23 = \frac{615}{161}

\frac{615}{7} /23

Convert element to fraction:

23 = \frac{23}{1}

= \frac{615}{7} \div \frac{23}{1}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{615}{7} \cdot \frac{1}{23}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{615 \cdot 1}{7 \cdot 23}

Multiply the numbers:

615 \cdot 1 = 615

= \frac{615}{7 \cdot 23}

Multiply the numbers:

7 \cdot 23 = 161

= \frac{615}{161}

= \frac{615}{161} \cdot 49/25 \cdot 53/27

\frac{615}{161} \cdot 49 = \frac{4305}{23}

\frac{615}{161} \cdot 49

Convert element to fraction:

49 = \frac{49}{1}

= \frac{615}{161} \cdot \frac{49}{1}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{615 \cdot 49}{161 \cdot 1}

Cancel

\frac{615 \cdot 49}{161 \cdot 1} : \frac{4305}{23}

\frac{615 \cdot 49}{161 \cdot 1}

Multiply the numbers:

161 \cdot 1 = 161

= \frac{615 \cdot 49}{161}

Factor the number:

49 = 7 \cdot 7

= \frac{615 \cdot 7 \cdot 7}{161}

Factor the number:

161 = 7 \cdot 23

= \frac{615 \cdot 7 \cdot 7}{7 \cdot 23}

Cancel the common factor:

7

= \frac{615 \cdot 7}{23}

Multiply the numbers:

615 \cdot 7 = 4305

= \frac{4305}{23}

= \frac{4305}{23}

= \frac{4305}{23} /25 \cdot 53/27

\frac{4305}{23} /25 = \frac{861}{115}

\frac{4305}{23} /25

Convert element to fraction:

25 = \frac{25}{1}

= \frac{4305}{23} \div \frac{25}{1}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{4305}{23} \cdot \frac{1}{25}

Cross-cancel common factor:

5

4305, 25

Greatest Common Divisor (GCD)

Prime factorization of

4305 : 3 \cdot 5 \cdot 7 \cdot 41

4305

4305

divides by

34305 = 1435 \cdot 3

= 3 \cdot 1435

1435

divides by

51435 = 287 \cdot 5

= 3 \cdot 5 \cdot 287

287

divides by

7287 = 41 \cdot 7

= 3 \cdot 5 \cdot 7 \cdot 41

3, 5, 7, 41

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 5 \cdot 7 \cdot 41

Prime factorization of

25 : 5 \cdot 5

25

25

divides by

525 = 5 \cdot 5

= 5 \cdot 5

The prime factors common to

4305, 25

are

= 5

= \frac{861}{23} \cdot \frac{1}{5}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{861 \cdot 1}{23 \cdot 5}

Multiply the numbers:

861 \cdot 1 = 861

= \frac{861}{23 \cdot 5}

Multiply the numbers:

23 \cdot 5 = 115

= \frac{861}{115}

= \frac{861}{115} \cdot 53/27

\frac{861}{115} \cdot 53 = \frac{45633}{115}

\frac{861}{115} \cdot 53

Convert element to fraction:

53 = \frac{53}{1}

= \frac{861}{115} \cdot \frac{53}{1}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{861 \cdot 53}{115 \cdot 1}

Multiply the numbers:

861 \cdot 53 = 45633

= \frac{45633}{115 \cdot 1}

Multiply the numbers:

115 \cdot 1 = 115

= \frac{45633}{115}

= \frac{45633}{115} /27

\frac{45633}{115} /27 = \frac{15211}{1035}

\frac{45633}{115} /27

Convert element to fraction:

27 = \frac{27}{1}

= \frac{45633}{115} \div \frac{27}{1}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{45633}{115} \cdot \frac{1}{27}

Cross-cancel common factor:

3

45633, 27

Greatest Common Divisor (GCD)

Prime factorization of

45633 : 3 \cdot 7 \cdot 41 \cdot 53

45633

45633

divides by

345633 = 15211 \cdot 3

= 3 \cdot 15211

15211

divides by

715211 = 2173 \cdot 7

= 3 \cdot 7 \cdot 2173

2173

divides by

412173 = 53 \cdot 41

= 3 \cdot 7 \cdot 41 \cdot 53

3, 7, 41, 53

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 7 \cdot 41 \cdot 53

Prime factorization of

27 : 3 \cdot 3 \cdot 3

27

27

divides by

327 = 9 \cdot 3

= 3 \cdot 9

9

divides by

39 = 3 \cdot 3

= 3 \cdot 3 \cdot 3

The prime factors common to

45633, 27

are

= 3

= \frac{15211}{115} \cdot \frac{1}{9}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{15211 \cdot 1}{115 \cdot 9}

Multiply the numbers:

15211 \cdot 1 = 15211

= \frac{15211}{115 \cdot 9}

Multiply the numbers:

115 \cdot 9 = 1035

= \frac{15211}{1035}

= \frac{15211}{1035}

Convert improper fractions to mixed numbers:

\frac{15211}{1035} = 14 \frac{721}{1035}

\frac{15211}{1035} = 14

Remainder

721

\frac{15211}{1035}

Write the problem in long division format

1035 \overline{∣ 15211}

Divide

1521

1035

to get

1

Divide

1521

1035

to get

1

1 1035 \overline{∣ 15211}

Multiply the quotient digit

(1)

by the divisor

1035

1 1035 \overline{∣ 15211} \underline{1035}

Subtract

1035

from

1521

1 1035 \overline{∣ 15211} \underline{1035} 486

Bring down the next number of the dividend

1 1035 \overline{∣ 15211} \underline{1035} 4861

1 1035 \overline{∣ 15211} \underline{1035} 4861

Divide

4861

1035

to get

4

Divide

4861

1035

to get

4

14 1035 \overline{∣ 15211} \underline{1035} 4861

Multiply the quotient digit

(4)

by the divisor

1035

14 1035 \overline{∣ 15211} \underline{1035} 4861 \underline{4140}

Subtract

4140

from

4861

14 1035 \overline{∣ 15211} \underline{1035} 4861 \underline{4140} 721

14 1035 \overline{∣ 15211} \underline{1035} 4861 \underline{4140} 721

The solution for Long Division of

\frac{15211}{1035}

14

with remainder of

721

14 Remainder 721

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{15211}{1035} = 14 \frac{721}{1035}

= 14 \frac{721}{1035}

= 14 \frac{721}{1035}

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Frequently Asked Questions (FAQ)

What is 41/21*45/23*49/25*53/27 ?
The solution to 41/21*45/23*49/25*53/27 is 14 721/1035