แพ็กเกจ

ศูนย์การเรียนรู้ / เลขคณิตและจำนวน

Prime factors, GCD and LCM

Break numbers into primes, then use the prime factorisation to find the greatest common divisor and least common multiple.

อ่าน 1 นาทีอัปเดตเมื่อ 18 ตุลาคม 2569โดย Sumzo teamตรวจทานโดย Sumzo team

A prime number has exactly two factors: 1 and itself (2, 3, 5, 7, 11, …). Every whole number greater than 1 can be written as a product of primes in exactly one way.

Finding the prime factorisation

Divide by the smallest prime that goes in, and repeat with what is left until you reach 1.

ตัวอย่างพร้อมวิธีทำ

Prime factors of 360

Write 360 as a product of primes.

แสดงวิธีทำ
  1. Divide by 2 three times.
    360→180→90→45360 \to 180 \to 90 \to 45
  2. Divide by 3 twice, leaving the prime 5.
    45→15→545 \to 15 \to 5
  3. Collect the primes.
    360=23×32×5360 = 2^3 \times 3^2 \times 5

คำตอบ: 23×32×52^3 \times 3^2 \times 5, which has (3+1)(2+1)(1+1)=24(3+1)(2+1)(1+1) = 24 divisors

ตรวจสอบโดยระบบคณิตศาสตร์ของ Sumzo

GCD and LCM from prime factors

  • GCD (greatest common divisor, also called HCF): multiply the primes the numbers share, each to its lowest power.
  • LCM (least common multiple): multiply every prime that appears, each to its highest power.

ตัวอย่างพร้อมวิธีทำ

GCD and LCM of 12 and 18

Find the GCD and LCM of 12 and 18.

แสดงวิธีทำ
  1. Factorise both numbers.
    12=22×3,18=2×3212 = 2^2 \times 3,\quad 18 = 2 \times 3^2
  2. Lowest powers for the GCD, highest powers for the LCM.
    gcd⁡=2×3=6,lcm⁡=22×32=36\gcd = 2 \times 3 = 6,\quad \operatorname{lcm} = 2^2 \times 3^2 = 36

คำตอบ: GCD = 6, LCM = 36

ตรวจสอบโดยระบบคณิตศาสตร์ของ Sumzo

เครื่องคิดเลข

แบบฝึกหัด

ติดโจทย์ข้อไหน ถาม Sumzo AI