Arrange the following pairs of integers in ascending order based on the value of their Gre… — Armed Services Vocational Aptitude Battery (ASVAB)

Arrange the following pairs of integers in ascending order based on the value of their Greatest Common Factor (GCF).

1 $32$ and $40$
2 $36$ and $48$
3 $42$ and $56$
4 $45$ and $60$

Answer

The correct ascending order based on the Greatest Common Factor (GCF) is:

32

and

40

(GCF = 8),

36

and

48

(GCF = 12),

42

and

56

(GCF = 14),

45

and

60

(GCF = 15).

By evaluating the Greatest Common Factor for each pair, we find that the GCF of

32

and

40

8

; the GCF of

36

and

48

12

; the GCF of

42

and

56

14

; and the GCF of

45

and

60

15

. The correct ascending order is

8

12

14

15

Step-by-Step Solution

Find the GCF for

45

and

60

The GCF is

15

The factors of

45

are

1, 3, 5, 9, 15, 45

. The factors of

60

include

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

. The largest shared factor is

15

Find the GCF for

32

and

40

The GCF is

8

The largest number that divides exactly into both

32

and

40

8

Find the GCF for

42

and

56

The GCF is

14

The largest number that divides exactly into both

42

and

56

14

(

42 = 14 \times 3

56 = 14 \times 4

Find the GCF for

36

and

48

The GCF is

12

The largest number that divides exactly into both

36

and

48

12

Order the pairs based on the calculated GCFs.

The sequence from smallest to largest GCF is

8

12

14

15

Arranging the values in ascending order determines the correct sequence.

Key Concept

Calculating the Greatest Common Factor (GCF) of pairs of integers.

Alternative Method

You can also use prime factorization for each number to find the GCF by multiplying the lowest powers of all common prime factors between the pairs.

Estimated Time:1m 30s

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Answer

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Alternative Method

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