Identifying Three-Digit Numbers with 5 and 8 as Factors: An SEO-Optimized Guide

In this article, we will explore the process of finding three-digit numbers that have both 5 and 8 as factors. We will provide an in-depth explanation of how to find these numbers step-by-step, covering concepts such as least common multiple (LCM) and factors.

Understanding Factors

Before we dive into how to find a three-digit number with both 5 and 8 as factors, it's important to understand the concept of factors. A factor of a number is a divisor of that number. For example, the factors of 8 are 1, 2, 4, and 8 because these numbers divide 8 without leaving a remainder.

Factors of 5 and 8

Factors of 5: 5 is a prime number, so its only factors are 1 and 5.

Factors of 8: 8 can be expressed as ( 2^3 ), and its factors are 1, 2, 4, and 8.

Least Common Multiple (LCM) of 5 and 8

The least common multiple (LCM) of two or more numbers is the smallest number for which they are all factors. To find the LCM of 5 and 8, we calculate as follows:

LCM(5, 8) 51 × 23 5 × 8 40

Thus, the LCM of 5 and 8 is 40. This means that 40 is the smallest number that is a multiple of both 5 and 8.

Identifying Three-Digit Multiples of 40

To find all three-digit numbers that have 5 and 8 as factors, we need to find the three-digit multiples of 40. The smallest three-digit number is 100 and the largest is 999.

Smallest Three-Digit Multiple of 40

The smallest three-digit multiple of 40 can be found by dividing 100 by 40 and rounding up the result:

100 ÷ 40 2.5 → ?2.5? 3

Thus, the smallest three-digit multiple of 40 is:

3 × 40 120

Largest Three-Digit Multiple of 40

The largest three-digit multiple of 40 can be found by dividing 999 by 40 and rounding down the result:

999 ÷ 40 24.975 → ?24.975? 24

Thus, the largest three-digit multiple of 40 is:

24 × 40 960

List of Three-Digit Multiples of 40

Starting from 120 and ending at 960, the three-digit multiples of 40 are:

120 160 200 240 280 320 360 400 440 480 520 560 600 640 680 720 760 800 840 880 920 960

Any of these numbers, such as 120, 160, 200 etc., are three-digit numbers that have 5 and 8 as factors.

Conclusion

To summarize, any three-digit number that is divisible by 40 will have both 5 and 8 as factors. The list of such numbers includes 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600, 640, 680, 720, 760, 800, 840, 880, 920, and 960.

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