Highest Common Factor Properties And Methods To Calculate

What are the factors of 40?

Start dividing the given number 40 with the numbers which can divide 40 exactly, starting from 1.

The quotient obtained after each division will be one of the factor of 40.

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Divide 40 by 1

40 ÷ 1 = 40

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Divide 40 by 2

40 ÷ 2 = 20

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Divide 40 by 4

40 ÷ 4 = 10

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Divide 40 by 5

40 ÷ 5 = 8

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Divide 40 by 8

40 ÷ 8 = 5

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Divide 40 by 10

40 ÷ 10 = 4

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Divide 40 by 20

40 ÷ 20 = 2

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Divide 40 by 40

40 ÷ 40 = 1

The quotient obtained from the above divisions are 1, 2, 4, 5, 8, 10, 20 and 40.

∴ There are a total of eight factors of 40 i.e. 1, 2, 4, 5, 8, 10, 20 and 40.

Find the common factors of 4 and 10.

Step 1: Find out the factors of 4 and 10 separately.

Factors of 4:

$\frac{4}{1}=4$

$\frac{4}{2}=2$

$\frac{4}{4}=1$

There are a total of three factors of 4 viz. 1, 2 and 4.

Factors of 10:

$\frac{10}{1}=10$

$\frac{10}{2}=5$

$\frac{10}{5}=2$

$\frac{10}{10}=1$

There are a total of four factors of 10 viz. 1, 2, 5 and 10.

Step 2: Find out the common factors of 4 and 10.

Finally, we can say 1 and 2 are the common factors of 4 and 10, because the factors 1 and 2 do exist for both numbers 4 and 10.

Find the GCD of 12 and 20.

Step 1: Find out the factors of 12.

$\frac{12}{1}=12$

$\frac{12}{2}=6$

$\frac{12}{3}=4$

$\frac{12}{4}=3$

$\frac{12}{6}=6$

$\frac{12}{12}=1$

There are a total of six factors of 12 viz. 1, 2, 3, 4, 6 and 12.

Step 2: Find out the factors of 20.

$\frac{20}{1}=20$

$\frac{20}{2}=10$

$\frac{20}{4}=5$

$\frac{20}{5}=4$

$\frac{20}{10}=2$

$\frac{20}{20}=1$

There are a total of six factors of 20 viz. 1, 2, 4, 5, 10 and 20.

Step 3: Find out the common factors from the list of factors of each 12 and 20.

∴ the common factors are 1, 2 and 4.

Step 4: Find out the greatest number among those common factors, that would be the GCD of 12 and 20.

∴ the greatest number among the common factors 1, 2 and 4 is 4.

Hence, GCD of 12 and 20 is 4.

Find the HCF of 12 and 20 using prime factorization method.

Step 1: Split 12 and 20 into its factors

12 = 2 × 2 × 3 = 2² × 3

20 = 2 × 2 × 5 = 2² × 5

Step 2: Write the common prime factors obtained in step 2.

Here, the common prime factor is 2.

Step 3: Write the minimum number of times the common prime factor 2 occurs.

which is 2 times which is 2²

Step 4: Now multiply each common prime factor 2² that obtained in step 3.

2² = 2 × 2 = 4, which is the HCF of 12 and 20.

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Find the HCF of 84 and 48 using prime factorization method.

Step 1: Split 84 and 48 into its factors

84 = 2 × 2 × 3 × 7 = 2² × 3 × 7

48 = 2 × 2 × 2 × 2 × 3 = 2⁴ × 3

Step 2: Write the common prime factors obtained in step 2.

Here, the common prime factors are 2 and 3.

Step 3: Write the minimum number of times the common prime factors 2 and 3 occur.

which is 2² and 3¹.

Step 4: Now multiply each common prime factor 2² and 3 that obtained in step 3.

2² × 3 = 4 × 3 = 12

∴ HCF of 84 and 48 is 12.

Find GCD of 12 and 20 using division method.

Step 1: Write the smallest number and the largest number 12 and 20 respectively

Step 2: Divide the greatest number 20 by the smallest number 12, which gives 8 as remainder.

Step 3: If the remainder in step 2 is not 0, then go to step 4.

Step 4: Again divide the smallest number by the obtained remainder 8. Now, the remainder is 4. Repeat step 4 until the remainder becomes 0.

Divide 8 by 4. Finally the remainder becomes 0.

Hence, GCD is 4.

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Find HCF of 84 and 48 using the division method.

Step 1: Write the smallest number and the largest number 48 and 84 respectively

Step 2: Divide the greatest number 84 by the smallest number 48.

Step 3: Remainder is 36. So, go to step 4.

Step 4: Again divide 48 by remainder 36. Now, the remainder is 12. Repeat step 4 until the remainder is 0.

Divide 36 by 12 which gives the remainder 0.

Hence, HCF is 12.

What is the HCF of 20 and 50?

20 and 50 can exactly be divided by 10.

It means 10 is the HCF of 20 and 50.

HCF of two numbers 27 and 60 is 3.

It means the HCF 3 can't be greater than the two numbers 27 and 60

What is the HCF of 27 and 54?

27 and 54 are the given numbers.

Factors of 54 are 2 and 27.

So, the factor 27 is same as the one of the given numbers 27 and 54.

Also, 27 is the smallest number out of the two given numbers 27 and 54.

Therefore, HCF of 27 and 54 will be equal to the smallest number 27.

GCD of 14 and 17 is 1.

Because, 14 and 17 are coprimes numbers.

GCD of 19 and 20 is 1.

Because, 19 and 20 are consecutive numbers.

Why 6 is a perfect number?

∵ sum of factors of 6 is 12

and 6 × 2 = 12

Steps to find factors of 6

Step 1: Find out the factors of 6.

$\frac{6}{1}=6$

$\frac{6}{2}=3$

$\frac{6}{3}=2$

$\frac{6}{6}=1$

Factors of 6 are 1, 2, 3 and 6

Step 2: Find the sum of factors

1 + 2 + 3 + 6 = 12

∴ we can see, the sum of factors of 6 which is 12 is equal to twice the number itself.