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Understanding Congruences and Remainders

Understanding Congruences and Remainders

Assessment

Interactive Video

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•
CCSS
6.EE.A.1

Standards-aligned

Created by

Ethan Morris

FREE Resource

Standards-aligned

CCSS.6.EE.A.1
The video tutorial explains how to find the remainder when 3 to the power of 123 is divided by 7 using congruence. It presents two methods: the first involves expressing powers of 3 in terms of 3 squared and using congruences, while the second method uses 3 cubed and its congruence properties. Both methods ultimately show that the remainder is 6.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main mathematical concept used to solve the problem of finding the remainder when 3^123 is divided by 7?

Congruence

Factorization

Integration

Differentiation

Tags

CCSS.6.EE.A.1

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the first method, what is 3 squared congruent to mod 7?

1

4

2

3

Tags

CCSS.6.EE.A.1

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is 3^123 expressed in terms of 3 squared in the first method?

3 squared to the power of 62 times 3

3 squared to the power of 60 times 3

3 squared to the power of 61 times 3

3 squared to the power of 63 times 3

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is 2 cubed congruent to mod 7, which is used in the first method?

0

1

2

3

Tags

CCSS.6.EE.A.1

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the second method, what is 3 cubed congruent to mod 7?

8

6

5

7

Tags

CCSS.6.EE.A.1

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is 3^123 expressed in terms of 3 cubed in the second method?

3 cubed to the power of 40

3 cubed to the power of 41

3 cubed to the power of 42

3 cubed to the power of 43

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is 6 squared congruent to mod 7, which is used in the second method?

0

1

2

3

Tags

CCSS.6.EE.A.1

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