Math Problem Statement

Multiple math problems involving factors, divisibility, multiplication, and prime factorization.

Solution

I see you've uploaded images of math problems. I'll extract the content and solve the problems for you. Please hold on while I analyze the images. PIL import Image import pytesseract

Load the images

image_path1 = "/mnt/data/1737037837345mjek0hb1.jpg" image_path2 = "/mnt/data/17370378373465kxr99v5.jpg"

Use OCR to extract text

text1 = pytesseract.image_to_string(Image.open(image_path1)) text2 = pytesseract.image_to_string(Image.open(image_path2))

text1, text2### Problems Extracted:

Image 1:

  1. A number is greater than 48248^2 and less than 49249^2. If 626^2 is one of its factors and it is a multiple of 13, what is the number?
  2. Given a six-digit number 328xyz328xyz, find the values of x,y,zx, y, z such that the number is divisible by 3, 4, and 5, and is the smallest six-digit number starting with 328 that has this property. How many other numbers have this property?
  3. When multiplying a number by 11, a special method is used:
    • Write the last digit of the number.
    • Work right to left, summing adjacent digits and carrying correctly.
    • Write the first digit.
      Example: 5389×11=5912795389 \times 11 = 591279.
      Tasks:
    • Perform this method for:
      • 17089×1117089 \times 11
      • 2223×112223 \times 11
      • 1654998×111654998 \times 11
      • 1654998×1111654998 \times 111
    • Briefly explain why this method works.
  4. Find a three-digit number that leaves a remainder of 1 when divided by 2, 3, 4, 5, or 6, and no remainder when divided by 7.
  5. If the total hours worked by employees on Thursday is 133, and each employee works the same number of hours daily, how many employees work on Thursday?

Image 2:

  1. The product of two consecutive page numbers is 1190. What are the two pages?
  2. What time will it be 23,999,999,99623,999,999,996 hours after 7 p.m.?
  3. Find the smallest whole number divisible by 11 that leaves a remainder of 1 when divided by numbers 2 through 10.
  4. What is the largest prime factor of 9309393093?
  5. The product of two whole numbers is 10,000,00010,000,000. Neither is a multiple of 10. What are the numbers?
  6. A teacher multiplied the ages of her students and got 15,231,236,267,52015,231,236,267,520.
    • a. Find the prime factorization of the number.
    • b. Use this to determine the students' ages and the number of students of each age.

I'll start solving these problems one by one. Let me know if you have a specific one you'd like me to prioritize!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Number Theory
Divisibility Rules
Prime Factorization
Arithmetic Multiplication

Formulas

Divisibility rules for 2, 3, 4, 5, 6, and 11
Prime factorization techniques
Properties of consecutive numbers: n(n+1)

Theorems

Fundamental Theorem of Arithmetic
Least Common Multiple and Greatest Common Divisor principles

Suitable Grade Level

Grade 8-10