Multiples of 60

Created by: Team Maths - Examples.com, Last Updated: May 24, 2024

Multiples of 60

Multiples of 60 are numbers that can be expressed as 60 times an integer. These numbers are also known as even numbers. Starting from 60, they follow a consistent pattern, increasing by 60 each time (e.g., 60, 120, 180, 240, 300, etc.). Multiples of 60 play a fundamental role in arithmetic and number theory, forming the basis for understanding even and odd numbers and serving as building blocks for more complex mathematical concepts. Recognizing and working with multiples of 60 is essential for performing various arithmetic operations efficiently.

What are Multiples of 60?

Multiples of 60 are numbers that can be expressed as 60×n, where n is an integer. These numbers are always even and include values like 60, 120, 180, 240, and so on.

Prime Factorization of 60:2 × 2 × 3 × 5

First 10 Multiples of 60 are 60, 120, 180, 240, 300, 360, 420, 480, 540, 600

First 50 Multiples of 60 are 60, 120, 180, 240, 300, 360, 420, 480, 540, 600, 660, 720, 780, 840, 900, 960, 1020, 1080, 1140, 1200, 1260, 1320, 1380, 1440, 1500, 1560, 1620, 1680, 1740, 1800, 1860, 1920, 1980, 2040, 2100, 2160, 2220, 2280, 2340, 2400, 2460, 2520, 2580, 2640, 2700, 2760, 2820, 2880, 2940, 3000

Table of 60

Important Notes

Even Numbers : All multiples of 60 are even numbers. This means they end in 0, 2, 4, 6, or 8.

Divisibility : A number is a multiple of 60 if it can be divided by 60 with no remainder.

Factors : Multiples of 60 have 60 as one of their factors. Additionally, they also have 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30 as factors since these are the factors of 60.

Infinite Sequence : There are infinitely many multiples of 60, extending indefinitely as 60, 120, 180, 240, 300, and so on.

Arithmetic Pattern : The difference between consecutive multiples of 60 is always 60.

Examples on Multiples of 60

Simple Multiples:

• 60: 60 × 1 = 60
• 120: 60 × 2 = 120
• 180: 60 × 3 = 180

Larger Multiples:

• 300: 60 × 5 = 300
• 600: 60 × 10 = 600
• 1200: 60 × 20 = 1200

Very Large Multiples:

• 3000: 60 × 50 = 3000
• 6000: 60 × 100 = 6000
• 12000: 60 × 200 = 12000

Real-Life Examples

Time:

60 seconds in a minute: This is a multiple of 60 because 60 × 1 = 60.

Money:

• \$60: This is a multiple of 60 because 60 × 1 = 60. (For example, 6 ten-dollar bills)

Measurements:

• 60 inches: This is a multiple of 60 because 60 × 1 = 60. (For example, 5 feet, as each foot is 12 inches)

Cycles and Periods:

• 60 minutes in an hour: This is a multiple of 60 because 60 × 1 = 60.

Angles:

• 60 degrees: An angle of 60 degrees is a multiple of 60 because 60 × 1 = 60. This is one of the angles in an equilateral triangle.

Practical Examples of Multiples of 60

If a recipe requires you to bake a cake for 180 minutes, how many hours do you need to bake it?

180 minutes is a multiple of 60 (180 ÷ 60 = 3). You need to bake the cake for 3 hours.

You are planning a road trip, and you know that you travel 60 miles every hour. How far will you have traveled after 5 hours?

60 miles per hour multiplied by 5 hours is 60 × 5 = 300 miles. You will have traveled 300 miles.

You are doing a workout routine that includes 60 push-ups in total. If you do sets of 15 push-ups each, how many sets do you need to complete?

60 push-ups divided by 15 push-ups per set is 60 ÷ 15 = 4 sets. You need to complete 4 sets.

A movie marathon lasts for 360 minutes. How many hours is the marathon?

360 minutes is a multiple of 60 (360 ÷ 60 = 6). The movie marathon lasts for 6 hours.

Practical Applications

Counting by Sixties: When counting by sixties (60, 120, 180, 240…), you are listing the multiples of 60.

Time Measurement: Any multiple of 60, such as 120 minutes or 360 seconds, represents a common time measurement because they are evenly divisible by 60.

Monetary Calculation: Any monetary value that is a multiple of 60, such as \$180 or \$300, can be easily divided into smaller units of \$60.

Can a negative number be a multiple of 60?

Yes, negative numbers can be multiples of 60, such as -60, -120, -180, etc.

Is 100 a multiple of 60?

No, 100 is not a multiple of 60 because 100 ÷ 60 = 1.6667, which is not an integer.

What is the sum of the first three multiples of 60?

The sum of the first three multiples of 60 is 60 + 120 + 180 = 360.

Are multiples of 60 divisible by 12?

Yes, multiples of 60 are divisible by 12 because 60 is a multiple of 12.

How many multiples of 60 are there between 1 and 1000?

There are 16 multiples of 60 between 1 and 1000 (60 × 1 to 60 × 16).

Is 720 a multiple of 60?

Yes, 720 is a multiple of 60 because 720 ÷ 60 = 12.

What is the greatest multiple of 60 less than 500?

The greatest multiple of 60 less than 500 is 480 (60 × 8 = 480).

How do multiples of 60 relate to time?

Multiples of 60 are used in time measurements, such as seconds in a minute and minutes in an hour.

What is the least common multiple (LCM) of 60 and 90?

The least common multiple of 60 and 90 is 180.

Can multiples of 60 be prime numbers?

No, multiples of 60 cannot be prime numbers because they have more than two factors.

What is the product of the first two multiples of 60?

The product of the first two multiples of 60 is 60 × 120 = 7200.

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