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Question

What is the quotient and remainder when $ 3487690123 $ is divided by $ 67 $ ?

Answer

The quotient is 52055076 and the remainder is 31.

Explanation

Division Table
		0	0	5	2	0	5	5	0	7	6
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9
				–	3	3	5
						3	4	0
					–	3	3	5
								5	1
								–	0
								5	1	2
							–	4	6	9
									4	3	3
								–	4	0	2
										3	1

STEP 0: set up a division table

6	7	3	4	8	7	6	9	0	1	2	3

STEP 1: DIVIDE 3 : 67 = 0 with a remainder of 3
		0
6	7	3	4	8	7	6	9	0	1	2	3

STEP 2: MULTIPLY 0 · 67 = 0
		0
6	7	3	4	8	7	6	9	0	1	2	3
		0

STEP 3: SUBTRACT 3 - 0 = 3
		0
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3

STEP 4: BRING DOWN
		0
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4

STEP 5: DIVIDE 34 : 67 = 0 with a remainder of 34
		0	0
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4

STEP 6: MULTIPLY 0 · 67 = 0
		0	0
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
			0

STEP 7: SUBTRACT 34 - 0 = 34
		0	0
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4

STEP 8: BRING DOWN
		0	0
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8

STEP 9: DIVIDE 348 : 67 = 5 with a remainder of 13
		0	0	5
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8

STEP 10: MULTIPLY 5 · 67 = 335
		0	0	5
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
		3	3	5

STEP 11: SUBTRACT 348 - 335 = 13
		0	0	5
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3

STEP 12: BRING DOWN
		0	0	5
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7

STEP 13: DIVIDE 137 : 67 = 2 with a remainder of 3
		0	0	5	2
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7

STEP 14: MULTIPLY 2 · 67 = 134
		0	0	5	2
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
			1	3	4

STEP 15: SUBTRACT 137 - 134 = 3
		0	0	5	2
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3

STEP 16: BRING DOWN
		0	0	5	2
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6

STEP 17: DIVIDE 36 : 67 = 0 with a remainder of 36
		0	0	5	2	0
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6

STEP 18: MULTIPLY 0 · 67 = 0
		0	0	5	2	0
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
						0

STEP 19: SUBTRACT 36 - 0 = 36
		0	0	5	2	0
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6

STEP 20: BRING DOWN
		0	0	5	2	0
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9

STEP 21: DIVIDE 369 : 67 = 5 with a remainder of 34
		0	0	5	2	0	5
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9

STEP 22: MULTIPLY 5 · 67 = 335
		0	0	5	2	0	5
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9
					3	3	5

STEP 23: SUBTRACT 369 - 335 = 34
		0	0	5	2	0	5
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9
				–	3	3	5
						3	4

STEP 24: BRING DOWN
		0	0	5	2	0	5
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9
				–	3	3	5
						3	4	0

STEP 25: DIVIDE 340 : 67 = 5 with a remainder of 5
		0	0	5	2	0	5	5
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9
				–	3	3	5
						3	4	0

STEP 26: MULTIPLY 5 · 67 = 335
		0	0	5	2	0	5	5
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9
				–	3	3	5
						3	4	0
						3	3	5

STEP 27: SUBTRACT 340 - 335 = 5
		0	0	5	2	0	5	5
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9
				–	3	3	5
						3	4	0
					–	3	3	5
								5

STEP 28: BRING DOWN
		0	0	5	2	0	5	5
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9
				–	3	3	5
						3	4	0
					–	3	3	5
								5	1

STEP 29: DIVIDE 51 : 67 = 0 with a remainder of 51
		0	0	5	2	0	5	5	0
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9
				–	3	3	5
						3	4	0
					–	3	3	5
								5	1

STEP 30: MULTIPLY 0 · 67 = 0
		0	0	5	2	0	5	5	0
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9
				–	3	3	5
						3	4	0
					–	3	3	5
								5	1
									0

STEP 31: SUBTRACT 51 - 0 = 51
		0	0	5	2	0	5	5	0
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9
				–	3	3	5
						3	4	0
					–	3	3	5
								5	1
								–	0
								5	1

STEP 32: BRING DOWN
		0	0	5	2	0	5	5	0
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9
				–	3	3	5
						3	4	0
					–	3	3	5
								5	1
								–	0
								5	1	2

STEP 33: DIVIDE 512 : 67 = 7 with a remainder of 43
		0	0	5	2	0	5	5	0	7
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9
				–	3	3	5
						3	4	0
					–	3	3	5
								5	1
								–	0
								5	1	2

STEP 34: MULTIPLY 7 · 67 = 469
		0	0	5	2	0	5	5	0	7
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9
				–	3	3	5
						3	4	0
					–	3	3	5
								5	1
								–	0
								5	1	2
								4	6	9

STEP 35: SUBTRACT 512 - 469 = 43
		0	0	5	2	0	5	5	0	7
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9
				–	3	3	5
						3	4	0
					–	3	3	5
								5	1
								–	0
								5	1	2
							–	4	6	9
									4	3

STEP 36: BRING DOWN
		0	0	5	2	0	5	5	0	7
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9
				–	3	3	5
						3	4	0
					–	3	3	5
								5	1
								–	0
								5	1	2
							–	4	6	9
									4	3	3

STEP 37: DIVIDE 433 : 67 = 6 with a remainder of 31
		0	0	5	2	0	5	5	0	7	6
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9
				–	3	3	5
						3	4	0
					–	3	3	5
								5	1
								–	0
								5	1	2
							–	4	6	9
									4	3	3

STEP 38: MULTIPLY 6 · 67 = 402
		0	0	5	2	0	5	5	0	7	6
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9
				–	3	3	5
						3	4	0
					–	3	3	5
								5	1
								–	0
								5	1	2
							–	4	6	9
									4	3	3
									4	0	2

STEP 39: SUBTRACT 433 - 402 = 31
		0	0	5	2	0	5	5	0	7	6
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9
				–	3	3	5
						3	4	0
					–	3	3	5
								5	1
								–	0
								5	1	2
							–	4	6	9
									4	3	3
								–	4	0	2
										3	1

STEP 39: SUBTRACT 433 - 402 = 31
		0	0	5	2	0	5	5	0	7	6
6	7	3	4	8	7	6	9	0	1	2	3
	–	0
		3	4
		–	0
		3	4	8
	–	3	3	5
			1	3	7
		–	1	3	4
					3	6
					–	0
					3	6	9
				–	3	3	5
						3	4	0
					–	3	3	5
								5	1
								–	0
								5	1	2
							–	4	6	9
									4	3	3
								–	4	0	2
										3	1

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