GCF worksheet

1. Greatest common factor: 10

1. Use Euclid's method (the Euclidean algorithm). Divide the larger number by the smaller and keep the remainder. Then repeat with the smaller number and the remainder until nothing is left over

   $\text{gcf(50, 190)}$

2. Division 1: 190 ÷ 50 leaves a remainder of 40

   $190$$=3\times 50+40$

3. Division 2: 50 ÷ 40 leaves a remainder of 10

   $50$$=1\times 40+10$

4. Division 3: nothing is left over, so the number you divided by, 10, is the GCF of the pair

   $40$$=4\times 10+0$

5. The GCF of the first pair

   $\text{gcf(50, 190)}$$=10$

6. Bring in the next number: find the GCF of the answer so far and that number

   $\text{gcf(10, 350)}$$=10$

2. Greatest common factor: 2

1. Use Euclid's method (the Euclidean algorithm). Divide the larger number by the smaller and keep the remainder. Then repeat with the smaller number and the remainder until nothing is left over

   $\text{gcf(38, 180)}$

2. Division 1: 180 ÷ 38 leaves a remainder of 28

   $180$$=4\times 38+28$

3. Division 2: 38 ÷ 28 leaves a remainder of 10

   $38$$=1\times 28+10$

4. Division 3: 28 ÷ 10 leaves a remainder of 8

   $28$$=2\times 10+8$

5. Division 4: 10 ÷ 8 leaves a remainder of 2

   $10$$=1\times 8+2$

6. Division 5: nothing is left over, so the number you divided by, 2, is the GCF of the pair

   $8$$=4\times 2+0$

7. The GCF of the first pair

   $\text{gcf(38, 180)}$$=2$

8. Bring in the next number: find the GCF of the answer so far and that number

   $\text{gcf(2, 250)}$$=2$

3. Greatest common factor: 45

1. Use Euclid's method (the Euclidean algorithm). Divide the larger number by the smaller and keep the remainder. Then repeat with the smaller number and the remainder until nothing is left over

   $\text{gcf(45, 180)}$

2. Division 1: nothing is left over, so the number you divided by, 45, is the GCF of the pair

   $180$$=4\times 45+0$

3. The GCF of the first pair

   $\text{gcf(45, 180)}$$=45$

4. Bring in the next number: find the GCF of the answer so far and that number

   $\text{gcf(45, 360)}$$=45$

4. Greatest common factor: 1

1. Use Euclid's method (the Euclidean algorithm). Divide the larger number by the smaller and keep the remainder. Then repeat with the smaller number and the remainder until nothing is left over

   $\text{gcf(38, 148)}$

2. Division 1: 148 ÷ 38 leaves a remainder of 34

   $148$$=3\times 38+34$

3. Division 2: 38 ÷ 34 leaves a remainder of 4

   $38$$=1\times 34+4$

4. Division 3: 34 ÷ 4 leaves a remainder of 2

   $34$$=8\times 4+2$

5. Division 4: nothing is left over, so the number you divided by, 2, is the GCF of the pair

   $4$$=2\times 2+0$

6. The GCF of the first pair

   $\text{gcf(38, 148)}$$=2$

7. Bring in the next number: find the GCF of the answer so far and that number

   $\text{gcf(2, 325)}$$=1$

5. Greatest common factor: 12

1. Use Euclid's method (the Euclidean algorithm). Divide the larger number by the smaller and keep the remainder. Then repeat with the smaller number and the remainder until nothing is left over

   $\text{gcf(48, 180)}$

2. Division 1: 180 ÷ 48 leaves a remainder of 36

   $180$$=3\times 48+36$

3. Division 2: 48 ÷ 36 leaves a remainder of 12

   $48$$=1\times 36+12$

4. Division 3: nothing is left over, so the number you divided by, 12, is the GCF of the pair

   $36$$=3\times 12+0$

5. The GCF of the first pair

   $\text{gcf(48, 180)}$$=12$

6. Bring in the next number: find the GCF of the answer so far and that number

   $\text{gcf(12, 300)}$$=12$

6. Greatest common factor: 5

1. Use Euclid's method (the Euclidean algorithm). Divide the larger number by the smaller and keep the remainder. Then repeat with the smaller number and the remainder until nothing is left over

   $\text{gcf(55, 250)}$

2. Division 1: 250 ÷ 55 leaves a remainder of 30

   $250$$=4\times 55+30$

3. Division 2: 55 ÷ 30 leaves a remainder of 25

   $55$$=1\times 30+25$

4. Division 3: 30 ÷ 25 leaves a remainder of 5

   $30$$=1\times 25+5$

5. Division 4: nothing is left over, so the number you divided by, 5, is the GCF of the pair

   $25$$=5\times 5+0$

6. The GCF of the first pair

   $\text{gcf(55, 250)}$$=5$

7. Bring in the next number: find the GCF of the answer so far and that number

   $\text{gcf(5, 260)}$$=5$

7. Greatest common factor: 5

1. Use Euclid's method (the Euclidean algorithm). Divide the larger number by the smaller and keep the remainder. Then repeat with the smaller number and the remainder until nothing is left over

   $\text{gcf(55, 220)}$

2. Division 1: nothing is left over, so the number you divided by, 55, is the GCF of the pair

   $220$$=4\times 55+0$

3. The GCF of the first pair

   $\text{gcf(55, 220)}$$=55$

4. Bring in the next number: find the GCF of the answer so far and that number

   $\text{gcf(55, 240)}$$=5$

8. Greatest common factor: 5

1. Use Euclid's method (the Euclidean algorithm). Divide the larger number by the smaller and keep the remainder. Then repeat with the smaller number and the remainder until nothing is left over

   $\text{gcf(40, 170)}$

2. Division 1: 170 ÷ 40 leaves a remainder of 10

   $170$$=4\times 40+10$

3. Division 2: nothing is left over, so the number you divided by, 10, is the GCF of the pair

   $40$$=4\times 10+0$

4. The GCF of the first pair

   $\text{gcf(40, 170)}$$=10$

5. Bring in the next number: find the GCF of the answer so far and that number

   $\text{gcf(10, 275)}$$=5$

9. Greatest common factor: 1

1. Use Euclid's method (the Euclidean algorithm). Divide the larger number by the smaller and keep the remainder. Then repeat with the smaller number and the remainder until nothing is left over

   $\text{gcf(33, 190)}$

2. Division 1: 190 ÷ 33 leaves a remainder of 25

   $190$$=5\times 33+25$

3. Division 2: 33 ÷ 25 leaves a remainder of 8

   $33$$=1\times 25+8$

4. Division 3: 25 ÷ 8 leaves a remainder of 1

   $25$$=3\times 8+1$

5. Division 4: nothing is left over, so the number you divided by, 1, is the GCF of the pair

   $8$$=8\times 1+0$

6. The GCF of the first pair

   $\text{gcf(33, 190)}$$=1$

7. Bring in the next number: find the GCF of the answer so far and that number

   $\text{gcf(1, 275)}$$=1$

10. Greatest common factor: 1

1. Use Euclid's method (the Euclidean algorithm). Divide the larger number by the smaller and keep the remainder. Then repeat with the smaller number and the remainder until nothing is left over

   $\text{gcf(73, 160)}$

2. Division 1: 160 ÷ 73 leaves a remainder of 14

   $160$$=2\times 73+14$

3. Division 2: 73 ÷ 14 leaves a remainder of 3

   $73$$=5\times 14+3$

4. Division 3: 14 ÷ 3 leaves a remainder of 2

   $14$$=4\times 3+2$

5. Division 4: 3 ÷ 2 leaves a remainder of 1

   $3$$=1\times 2+1$

6. Division 5: nothing is left over, so the number you divided by, 1, is the GCF of the pair

   $2$$=2\times 1+0$

7. The GCF of the first pair

   $\text{gcf(73, 160)}$$=1$

8. Bring in the next number: find the GCF of the answer so far and that number

   $\text{gcf(1, 320)}$$=1$