High School

Find the Highest Common Factor (HCF) of each pair of numbers:

a. 3 and 6
b. 24 and 16
c. 15 and 40
d. 42 and 70
e. 32 and 36
f. 26 and 36
g. 22 and 44
h. 42 and 48

Underline the factors that appear in both sets and pick out the highest underlined factor.

Answer :

Sure, let's find the Highest Common Factor (HCF) for each pair of numbers step-by-step. The Highest Common Factor is the largest factor that divides both of the numbers in the pair.

### a) 3 and 6
- Factors of 3: 1, 3
- Factors of 6: 1, 2, 3, 6
- The common factors are 1 and 3.
- HCF: 3

### b) 24 and 16
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 16: 1, 2, 4, 8, 16
- The common factors are 1, 2, 4, and 8.
- HCF: 8

### c) 15 and 40
- Factors of 15: 1, 3, 5, 15
- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
- The common factors are 1 and 5.
- HCF: 5

### d) 42 and 70
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
- The common factors are 1, 2, 7, and 14.
- HCF: 14

### e) 32 and 36
- Factors of 32: 1, 2, 4, 8, 16, 32
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- The common factors are 1, 2, and 4.
- HCF: 4

### f) 26 and 36
- Factors of 26: 1, 2, 13, 26
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- The common factors are 1 and 2.
- HCF: 2

### g) 22 and 44
- Factors of 22: 1, 2, 11, 22
- Factors of 44: 1, 2, 4, 11, 22, 44
- The common factors are 1, 2, 11, and 22.
- HCF: 22

### h) 42 and 48
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- The common factors are 1, 2, 3, and 6.
- HCF: 6

So, the HCFs for each pair of numbers are:
- a) 3
- b) 8
- c) 5
- d) 14
- e) 4
- f) 2
- g) 22
- h) 6

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