The number 21 is in a lot of places. If you are a gambler, you may think of 21 at a blackjack table. In the game, you start out with being dealt two cards. One card is face-up for everyone to see. The other card is face down. Only you can see that card.
Face cards are worth 10 points. Aces are worth either 1 or 11. You get to decide on that one. The other cards are worth the amount that is on the card. Your goal is to get to 21 or closest without going over.
Once you go over 21, you would lose…unless you bluff. Now, at this point with your two cards, you can get more cards, one at a time. At any point, you can stop if you think you might go over 21. Look at the two cards below.
Do you know how you could get a perfect blackjack amount of 21? The seven card is face up for everyone to see. This would require for you to know the factors of 21.
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Factors of 21 are 1, 3, 7, and 21
Look at the images below. They show two groupings. These have to do with the factors of 21.
This image shows several game pieces. Each set of game pieces has 3 in it. Then there are 7 groups. So, the factors for 21 are 3 and 7. It can also be grouped the other way around.
This also shows the factors of 21.
Now, back to our blackjack game. You have a seven. How could you get a perfect blackjack score of 21 with your other two cards? This has to do with the other two cards. We know that 3 groups of 7 equals 21, and so each of the other two cards would need to be sevens.
Therefore, we know that the factors of 21 are 3 and 7. However, 1 and 21 are also factors of 21. All of the factors would be 1, 3, 7, and 21.
Challenging Questions
Question 1List the factors of 21
Which positive whole numbers divide 21 without leaving a remainder?
The factors of 21 are 1, 3, 7, 21.
Each listed number divides the original number evenly.
Question 2Find the factor pairs of 21
Which multiplication pairs have a product of 21?
21 has these positive factor pairs: 1 × 21; 3 × 7.
Multiplying the two numbers in any pair gives the original number.
Question 3Prime-factorize 21
What is the prime factorization of 21?
21 = 3 × 7.
Every number in the product is prime.
