Finding Pairs with a Given GCF
Finding Pairs with a Given GCF is a skill on Pengi from Lesson 5: Greatest Common Factor in Big Ideas Math, Advanced 1.
Key Concepts
Property To find a pair of numbers with a specific greatest common factor (GCF), multiply the GCF by two numbers that are coprime. Two numbers are coprime if their only common factor is 1. If $g$ is the desired GCF, the pair can be found by calculating $(g \cdot x)$ and $(g \cdot y)$, where $\text{GCF}(x, y) = 1$.
Examples Which pair of numbers has a GCF of 7? The pair $(14, 21)$ has a GCF of 7. This is because $14 = 7 \cdot 2$ and $21 = 7 \cdot 3$, and the numbers 2 and 3 are coprime. Find a pair of numbers with a GCF of 12. Choose two coprime numbers, like 3 and 5. The pair is $(12 \cdot 3, 12 \cdot 5)$, which is $(36, 60)$. The GCF of 36 and 60 is 12.
Explanation This skill involves working backward from a known greatest common factor (GCF). To construct a pair of numbers with a specific GCF, you must ensure two conditions are met. First, both numbers in the pair must be multiples of the desired GCF. Second, the factors you multiply the GCF by must not share any common factors other than 1, otherwise, the GCF of the resulting pair would be larger than intended.
Common Questions
What is Finding Pairs with a Given GCF?
Finding Pairs with a Given GCF is a skill on Pengi from Lesson 5: Greatest Common Factor in Big Ideas Math, Advanced 1.
What grade level is Finding Pairs with a Given GCF for?
Finding Pairs with a Given GCF is part of the Grade 6 Math curriculum, covered in Big Ideas Math, Advanced 1. It is designed for students studying Math at the Grade 6 level.
How can I learn Finding Pairs with a Given GCF?
Pengi offers an AI-guided lesson for Finding Pairs with a Given GCF that walks you through the key concepts step by step. The lesson is aligned to Big Ideas Math, Advanced 1 so the content matches what you see in class.
How do I practice Finding Pairs with a Given GCF?
After learning the concept, use the Practice mode to work through targeted exercises on Finding Pairs with a Given GCF. The AI adapts to your level and gives feedback on each answer so you can identify and fix mistakes.
Which textbook covers Finding Pairs with a Given GCF?
Finding Pairs with a Given GCF is covered in Big Ideas Math, Advanced 1, specifically in Chapter 1: Numerical Expressions and Factors under Lesson 5: Greatest Common Factor. Pengi's lesson is aligned directly to this textbook so you can follow along with your class.
Is Finding Pairs with a Given GCF free to study on Pengi?
Yes, the core Learn and Practice modes for Finding Pairs with a Given GCF are available for free on Pengi. No credit card is required to start studying.