What are 3 consecutive positive integers?
Three consecutive positive integers are numbers like 4, 5, 6 that follow one after another without gaps, each one exactly one larger than the previous.
Pick any integer n, and the next two in line are n+1 and n+2. Works just as well with 1 or 100. These numbers pop up everywhere—house numbers, calendar dates, even the pages in your favorite book. They’re basically the building blocks of basic counting.
What is the smallest of 3 consecutive positive integers if the product of the smaller two integers is 5 less than 5 times the largest integer?
The smallest integer is 5, forming the sequence 5, 6, 7
Let’s set this up properly. If the numbers are x, x+1, and x+2, the equation becomes x(x+1) = 5(x+2) − 5. Solve that and you get x = 5. Quick check: 5×6 = 30, and 5×7 = 35, which is exactly 5 more than 30. That matches the “5 less than 5 times the largest” condition perfectly.
What is the product of three consecutive integers?
The product of any three consecutive integers is always divisible by 6
Why? In any trio like 4, 5, 6, one number is even (divisible by 2) and one is divisible by 3. Multiply those factors together—2 × 3 = 6—and the whole product must be divisible by 6. Take 4×5×6 = 120. Divide by 6 and you get 20, a clean integer. Honestly, this is one of those neat number theory tricks that always impresses.
How do you find the product of three consecutive numbers?
Multiply the three numbers together in order
Start with any three in a row, like 3, 4, 5. First multiply 3 × 4 = 12, then 12 × 5 = 60. No fancy formulas needed—just straightforward multiplication. This approach works for any trio of consecutive integers, whether you're dealing with small numbers or large ones.
What are two consecutive positive integers?
Two consecutive positive integers are pairs like 17 and 18 that differ by exactly 1
They’re everywhere—house numbers on a street, pages in a book, even the numbers on a clock face. Algebraically, you can write them as n and n+1, where n is any positive whole number. Recognizing these pairs is a handy skill for solving puzzles and word problems.
What are 2 consecutive odd numbers?
Two consecutive odd numbers differ by 2, such as 7 and 9
Odd numbers skip even numbers entirely. After 11 comes 13, not 12. This gap of 2 is useful in everything from number theory to arranging objects or seating people in alternating patterns. It’s a simple but powerful concept.
What are consecutive integers examples?
Examples include -4, -3, -2, 10, 11, 12, and 100, 101, 102
Consecutive integers can be negative, zero, or positive—they always follow one after another without skipping. You’ll find them in sequences, algorithms, and even when measuring time intervals or distances on a number line. They’re the backbone of orderly counting.
What is the product of three negative integers?
The product of three negative integers is always negative
Here’s why: two negatives make a positive, but multiplying that positive by a third negative flips the sign back to negative. Try it: (-2) × (-3) × (-4) = -24. This rule pops up in polynomial signs and physics when dealing with negative vectors.
Is it true that product of 3 consecutive natural numbers is always divisible by 6? Justify?
Yes, it’s always divisible by 6
In any three consecutive natural numbers, one is even (divisible by 2) and one is divisible by 3. Since 2 and 3 are prime and share no common factors, their product (6) must divide the overall product. Look at 3×4×5=60. Divide by 6 and you get 10—no remainder. This property is gold in modular arithmetic and number theory proofs.
Is the product of 3 consecutive numbers divisible by 6?
Yes, the product is always divisible by 6
No matter where you start, three consecutive integers will always include a multiple of 2 and a multiple of 3. That guarantees the product is divisible by 6. It works for positive numbers, negative numbers, and even sequences that include zero.
What three consecutive odd numbers have a product of 15525?
The numbers are 23, 25, and 27
These three odd numbers in a row multiply to 15,525. Check it: 23 × 25 = 575, then 575 × 27 = 15,525. Problems like this often appear in math competitions and number puzzles—good practice for sharpening your multiplication skills.
What happens when you add 3 consecutive numbers?
The sum is always 3 times the middle number
Try it: 7 + 8 + 9 = 24, and 3 × 8 = 24. It works because the smallest number is one less than the middle, and the largest is one more. So they cancel out: (n−1) + n + (n+1) = 3n. This is a neat mental math shortcut you can use anywhere.
What three consecutive integers have a sum of 72?
The numbers are 23, 24, and 25
If the total is 72, divide by 3 to find the middle number: 72 ÷ 3 = 24. That gives you the sequence 23, 24, 25. This trick works because three consecutive numbers are evenly spaced, so their average is the middle one—no algebra required.
What is the product of three negative integers?
The product is a negative integer
Multiply three negatives together and the result is always negative. Two negatives make a positive, but multiplying that positive by a third negative flips the sign. For example, (-2) × (-3) × (-4) = -24. This rule is essential when working with polynomials or negative vectors in physics.
What is the smallest of 3 consecutive positive integers if the product of the smaller two integers is 5 less than 5 times the largest integer *?
The smallest integer is 5, forming the sequence 5, 6, 7
Set up the equation properly. With numbers x, x+1, and x+2, we get x(x+1) = 5(x+2) − 5. Solving gives x = 5. Verify: 5×6 = 30, and 5×7 = 35. The difference is exactly 5, matching the condition perfectly.
What is the product of three negative integers?
The product is a negative integer
Three negatives multiplied together always give a negative result. Two negatives make a positive, but multiplying by a third negative flips the sign back. For instance, (-2) × (-3) × (-4) = -24. This pattern holds true every time.
Is it true that product of 3 consecutive natural numbers is always divisible by 6? Justify?
Yes, the product is always divisible by 6
In any three consecutive natural numbers, one must be divisible by 2 and another by 3. Since 2 and 3 are prime factors with no overlap, their product (6) must divide the overall product. Take 3×4×5=60. Divide by 6 and you get 10—no remainder. This is a fundamental property in number theory.
