Math - Check this Answer

1. Mom- Age 58 Middle Daughter – Age 4

2. Mom- Age 58

2x29= 58 or 58/2= 29, so the prime factorization is 29

Middle daughter- Age 4

22 or 2x2= 4, so the prime factorization is 2

Self- Age 32

25 or 2x2x2x2x2 or 32/2 =16, 16/2=8, 8/2=4, 4/2=2; thus 2 is the prime factorization

3. Lowest Common Multiple (LCM)

Taking all three original numbers (58,4,and 32) and dividing them by 2 is how I arrived at my answer of 928, which is the least common whole number amongst all three.

58, 116, 174, 232, 290,348,406,464,522,580, 696,...928 (58x16=928)

4,8,12,16,20,24,28,32,36,40,44, 48,52,56,…232…928 (4x232=928)

32, 64,96,128,160,192, 224, 256, 288, 320,352, …928 (32x29=928)

4. Greatest Common Factors (GCF)

All of these numbers are divisible by 2; I simply arrived at this answer by multiplying by all original numbers starting with one in order to find the highest number that they had in common without creating a decimal.

Factors for 58- 1, 2, 29, 58

Factors for 4- 1, 2, 4

Factors for 32- 1, 2, 4, 8, 16, 32

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Jan 08, 2012

Prime Factorization, LCM, GCF
by: Staff

Question:

1. Mom- Age 58 Middle Daughter – Age 4

2. Mom- Age 58

2x29= 58 or 58/2= 29, so the prime factorization is 29

Middle daughter- Age 4

22 or 2x2= 4, so the prime factorization is 2

Self- Age 32

25 or 2x2x2x2x2 or 32/2 =16, 16/2=8, 8/2=4, 4/2=2; thus 2 is the prime factorization

3. Lowest Common Multiple (LCM)

Taking all three original numbers (58,4,and 32) and dividing them by 2 is how I arrived at my answer of 928, which is the least common whole number amongst all three.

58, 116, 174, 232, 290,348,406,464,522,580, 696,...928 (58x16=928)

4,8,12,16,20,24,28,32,36,40,44, 48,52,56,…232…928 (4x232=928)

32, 64,96,128,160,192, 224, 256, 288, 320,352, …928 (32x29=928)

4. Greatest Common Factors (GCF)

All of these numbers are divisible by 2; I simply arrived at this answer by multiplying by all original numbers starting with one in order to find the highest number that they had in common without creating a decimal.

Factors for 58- 1, 2, 29, 58

Factors for 4- 1, 2, 4

Factors for 32- 1, 2, 4, 8, 16, 32

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Answer:

2. Mom- Age 58

Prime Factorization means to find all the prime factors

Since 58 = 2*29, the prime the prime factorization is: 2, 29 (not just 29)

Middle daughter- Age 4

Since 2x2= 4, the prime factorization is: 2, 2

Self- Age 32

Since 32 = 2*2*2*2*2, the prime the prime factorization is: 2, 2, 2, 2, 2

3. Lowest Common Multiple (LCM) of 58, 4, and 32

You can find the LCM (least common multiple) using the prime factors which you have already computed

List the prime factors again, being careful to show the exponents associated with each:

58, prime factors = 2 * 29 = 2¹ * 29¹

4, prime factors = 2 * 2 = 2²

32, prime factors = 2*2*2*2*2 = 2⁵

All together, there are the only two different prime factors listed: 2, and 29

To compute the LCM:

Choose the 2 with the highest exponent: 2⁵
Choose the 29 with the highest exponent: 29¹

Multiply these two numbers together

LCM = 2⁵ * 29¹ = 928

LCM (least common multiple) for the values 58, 4, and 32 = 928

This is exactly the same answer you computed.

4. Greatest Common Factors (GCF)

You can also find the GCF (greatest common factor) using the same prime factors which you used to compute the LCM.

58, prime factors = 2 * 29

4, prime factors = 2 * 2

32, prime factors = 2*2*2*2*2

Which factors appear as a prime factor for all three numbers?

There is only one number which appears as one of the prime factors for all three numbers: 2

GCF (for the numbers 58, 4, and 32) = 2

Thanks for writing.
Staff

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Math - Check this Answer

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