Question

HCF of 360,2700,42000​

Answer 1

Answer:

Find the prime factorization of 360

360 = 2 × 2 × 2 × 3 × 3 × 5

Find the prime factorization of 2700

2700 = 2 × 2 × 3 × 3 × 3 × 5 × 5

To find the GCF, multiply all the prime factors common to both numbers:

Therefore, GCF = 2 × 2 × 3 × 3 × 5

GCF = 180

Answer 2

Answer:

The HCF of the 360, 2700, and 42000​ is 60.

Step-by-step explanation:

Given: The numbers are 360, 2700, and 42000​.

We have to find the HCF of the above numbers.

• As we know that, the greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

We are solving in the following way:

We have,

The numbers are 360, 2700, and 42000​.

The HCF of the above numbers will be:

First, we will find the factors of the given numbers.

The factors of 360 are: $1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360$

The factors of 2700 are: $1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, \\90, 100, 108, 135, 150, 180, 225, 270, 300, 450, 540, 675, 900, 1350, 2700$

The factors of 42000 are: $1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25,$$28, 30, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 100, 105, 112, 120, 125, 140,$ $150, 168, 175, 200, 210, 240, 250, 280, 300, 336, 350, 375, 400, 420, 500, 525, 560,$ $600, 700, 750, 840, 875, 1000, 1050, 1200, 1400, 1500, 1680, 1750, 2000, 2100,$ $2625, 2800, 3000, 3500, 4200, 5250, 6000, 7000, 8400, 10500, 14000, 21000, 42000$

From the above, we can see that 60 is the largest positive integer that divides each of the integers.

Therefore the greatest common factor(HCF) is 60.

Note:

Q.Find the HCF of 360, 2700, and 42000​.