1. Find HCF (GCF, GCD) of 30,40 using Prime Factorization Method

Solution:
Step-1: Prime factorization of `30,40` using factor by division method

2 30 3 15 5 5   1

2 40 2 20 2 10 5 5   1

Step-2: Write each number as a product of primes, matching primes vertically when possible

30	=	2			× 3	× 5
40	=	2	× 2	× 2		× 5

Step-3: Bring down the common factors in each column. The HCF is the product of these factors

30	=	2			× 3	× 5
40	=	2	× 2	× 2		× 5
HCF	=	2				× 5	= 10

`:.` HCF of `30,40` is `10`

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2. Find HCF (GCF, GCD) of 45,25 using Prime Factorization Method

Solution:
Step-1: Prime factorization of `45,25` using factor by division method

3 45 3 15 5 5   1

5 25 5 5   1

Step-2: Write each number as a product of primes, matching primes vertically when possible

45	=	3	× 3	× 5
25	=			5	× 5

Step-3: Bring down the common factors in each column. The HCF is the product of these factors

45	=	3	× 3	× 5
25	=			5	× 5
HCF	=			5		= 5

`:.` HCF of `45,25` is `5`

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3. Find HCF (GCF, GCD) of 50,120 using Prime Factorization Method

Solution:
Step-1: Prime factorization of `50,120` using factor tree method

50     2 25     5 5

120     2 60     2 30     2 15     3 5

Step-2: Write each number as a product of primes, matching primes vertically when possible

50	=	2				× 5	× 5
120	=	2	× 2	× 2	× 3	× 5

Step-3: Bring down the common factors in each column. The HCF is the product of these factors

50	=	2				× 5	× 5
120	=	2	× 2	× 2	× 3	× 5
HCF	=	2				× 5		= 10

`:.` HCF of `50,120` is `10`

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4. Find HCF (GCF, GCD) of 400,140 using Prime Factorization Method

Solution:
Step-1: Prime factorization of `400,140` using factor tree method

400     2 200     2 100     2 50     2 25     5 5

140     2 70     2 35     5 7

Step-2: Write each number as a product of primes, matching primes vertically when possible

400	=	2	× 2	× 2	× 2	× 5	× 5
140	=	2	× 2			× 5		× 7

Step-3: Bring down the common factors in each column. The HCF is the product of these factors

400	=	2	× 2	× 2	× 2	× 5	× 5
140	=	2	× 2			× 5		× 7
HCF	=	2	× 2			× 5			= 20

`:.` HCF of `400,140` is `20`

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5. Find HCF (GCF, GCD) of 30,40,50,60 using Prime Factorization Method

Solution:
Step-1: Prime factorization of `30,40,50,60` using factor by division method

2 30 3 15 5 5   1

2 40 2 20 2 10 5 5   1

2 50 5 25 5 5   1

2 60 2 30 3 15 5 5   1

Step-2: Write each number as a product of primes, matching primes vertically when possible

30	=	2			× 3	× 5
40	=	2	× 2	× 2		× 5
50	=	2				× 5	× 5
60	=	2	× 2		× 3	× 5

Step-3: Bring down the common factors in each column. The HCF is the product of these factors

30	=	2			× 3	× 5
40	=	2	× 2	× 2		× 5
50	=	2				× 5	× 5
60	=	2	× 2		× 3	× 5
HCF	=	2				× 5		= 10

`:.` HCF of `30,40,50,60` is `10`

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