Understanding the concept of integral multiples is crucial in mathematics. If you’re searching for “integral multiple meaning in Hindi,” you’ve come to the right place. This article will delve into the meaning, provide relevant examples, and address common questions surrounding this fundamental mathematical concept. We’ll explore how integral multiples relate to factors and divisibility, and provide clear explanations to solidify your understanding.
What Does Integral Multiple Mean?
An integral multiple of a number is the product of that number and any integer. In simpler terms, it’s a number that can be obtained by multiplying the original number by a whole number (positive, negative, or zero). In Hindi, integral multiple is often referred to as “पूर्णांक गुणज” (purnank gunaj).
For example, the integral multiples of 3 are …, -9, -6, -3, 0, 3, 6, 9, 12, … Notice that each of these numbers can be obtained by multiplying 3 by an integer (like -3, -2, -1, 0, 1, 2, 3, 4, and so on).
Integral Multiples, Factors, and Divisibility
The concepts of integral multiples, factors, and divisibility are interconnected. If a number ‘a’ is an integral multiple of ‘b’, then ‘b’ is a factor of ‘a’, and ‘a’ is divisible by ‘b’.
For instance, 12 is an integral multiple of 3. This means 3 is a factor of 12, and 12 is divisible by 3. Understanding this relationship strengthens your grasp of fundamental arithmetic.
How to Find Integral Multiples
Finding integral multiples of a number is straightforward. Simply multiply the number by different integers. Let’s say you want to find the first five positive integral multiples of 5. You would calculate:
- 5 x 1 = 5
- 5 x 2 = 10
- 5 x 3 = 15
- 5 x 4 = 20
- 5 x 5 = 25
Therefore, the first five positive integral multiples of 5 are 5, 10, 15, 20, and 25.
Why Are Integral Multiples Important?
Integral multiples play a significant role in various mathematical concepts, including fractions, least common multiples (LCM), and greatest common factors (GCF). They are essential for understanding divisibility rules and solving problems related to ratios and proportions.
Common Questions About Integral Multiples
1. Is zero an integral multiple of every number?
Yes, zero is an integral multiple of every number because any number multiplied by zero equals zero.
2. Can integral multiples be negative?
Yes, integral multiples can be negative. Multiplying a number by a negative integer results in a negative integral multiple.
3. What is the difference between a multiple and an integral multiple?
While the term “multiple” often implies an integral multiple, technically, a multiple can involve fractions or decimals. However, an “integral multiple” specifically refers to multiples that are integers.
Conclusion
Understanding the concept of integral multiples, represented as “पूर्णांक गुणज” (purnank gunaj) in Hindi, is fundamental in mathematics. This article has explained its meaning, provided clear examples, and explored its relationship with factors and divisibility. By grasping this concept, you lay a strong foundation for more complex mathematical principles.
FAQ
- What is an integral multiple in simple terms? An integral multiple is the product of a number and any whole number.
- How do you find the integral multiples of a number? Multiply the number by different integers (positive, negative, or zero).
- Is 0 an integral multiple? Yes, 0 is an integral multiple of every number.
- What is the Hindi word for integral multiple? “पूर्णांक गुणज” (purnank gunaj)
- Why are integral multiples important? They are essential for understanding divisibility, fractions, LCM, GCF, and more.
- Can integral multiples be negative? Yes, multiplying a number by a negative integer results in a negative integral multiple.
- What’s the difference between a multiple and an integral multiple? An integral multiple is specifically a whole number multiple.
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