Listen to live Sportsound commentary from Ibrox
FT: Rangers 2-0 Ayr United - Barisic nets deflected opener & Silva doubles lead in closing stages
FT: Partick Thistle 2-3 Livingston - McInroy & Fitzpatrick strike put hosts two up before Nouble double forces extra time & Yengi scores in 120th minute
FT: Aberdeen 2-0 Bonnyrigg Rose - Miovski tucks in opener against fourth-tier visitors then volleys second
FT: Inverness CT 1-3 Hibs - Maolida nets deflected second-half strike then Boyle & Youan extend lead before Doran's late reply
FT: Kilmarnock 2-0 Cove Rangers - Van Veen hits bar for hosts before Watkins scores opener on stroke of half-time & Armstrong drills second
Championship: Dunfermline 0-3 Queen's Park
Remaining two Scottish Cup last-16 ties take place on Sunday
Draw for quarter-finals on Sunday Sportscene, BBC One Scotland (16:30 GMT) before Airdrie v hearts
Enjoy the remainder of your Saturday, troops.
Remember to tune in to Sportscene at 22:30 GMT on BBC One Scotland.
We'll be back tomorrow with more cup drama.
In the meantime, take care. 🤝
FT: Rangers 2-0 Ayr United
Rangers manager Philippe Clement has been speaking to BBC Scotland after his side progressed to the quarter-finals.
On performance: "We had full control for the 90 minutes. On a lucky day, we score four, five, six.
"It was a mature performance from the team and the most positive thing was we could give minutes to the players who have just come in and players who have been injured."
On Oscar Cortes: "We saw why we brought him here. It's clear from the first training session that he can help us."
On relationship with support: "You need to deserve that with what you do on the pitch. The fans here are incredibly loyal and incredibly fanatic. It gives a good signal to the team that the fans are behind them."
Image source, SNSWe've also got quotes from Rangers boss Philippe Clement coming right up.
We'll give the Belgian the final word...
FT: Rangers 2-0 Ayr Utd
Ayr United boss Scott Brown tells BBC Scotland: "We stuck by our guns, we had a game plan. The young ones did really well today.
"The lads couldn't hear us on the touchline so they had to do it themselves. We've been in three weeks, the lads have taken the information on really well.
"They expressed themselves really well. We need to get points on the board now. The league's the priority."
On referee Willie Collum showing him a yellow card: "It was only a matter of time. He should've sent off Fabio Silva for his second tackle. It's a pressure situation, people can't deal with it."
FT: Aberdeen 2-0 Bonnyrigg Rose
Watch Bojan Miovski's double against Bonnyrigg Rose as Aberdeen progress to last eight
Bojan Miovski scores a first-half double as Aberdeen beat League 2 Bonnyrigg to reach the Scottish Cup quarter-finals.
Read MoreWe've got two Sunday belters to round off quarter-final weekend:
We'll provide live text coverage of both games and you'll be able to watch the tie in Airdrie live on Sportscene.
You can watch the best of the last-16 action so far on Sportscene later.
BBC One Scotland is the channel you're after.
Be there for 22:30 GMT.
FT: Partick Thistle 2-3 Livingston
Watch Livingston complete sensational comeback with Tete Yengi's extra-time winner at Partick Thistle
FT: Rangers 2-0 Ayr Utd
Image source, SNS
Image source, SNS
Image source, SNSYou'll catch that live on Sportscene's pre-match coverage tomorrow prior to Airdrieonians v Hearts.
Tune in from 16:30 GMT on BBC One Scotland.
FT: Rangers 2-0 Ayr United
Martin Dowden
BBC Sport Scotland at Ibrox
Rangers progress and in cup football that's all the matters. Results just keep coming for Philippe Clement.
The outcome wasn't settled until Fabio Silva's late strike and that's down to an impressive overall Ayr United display.
They were a credit to the Championship and looked more like a Premiership side at times, particularly given how early they conceded but stayed they strong.
It wasn't quite the formality most expected but it's Rangers who take another positive step forward.
Goals from Borna Barisic and Fabio Silva send Rangers through to the last eight of the Scottish Cup.
Had Ben Dempsey taken a glorious chance early in the second half, the game could have been a different one.
But it wasn't to be for a well-drilled Ayr side as Rangers' treble dream remains alive.
Image source, SNSFabio Silva smashes in Rangers' second
Rangers 2-0 Ayr Utd
Rangers are just passing it about.
Rangers 2-0 Ayr Utd
Got no idea where these five added minutes came from, by the way.
Rangers 2-0 Ayr Utd
This feels very much like a formality for Rangers now.
They will be the sixth team in the quarter-final draw.
Rangers 2-0 Ayr Utd
Five minutes of stoppage time.
Rangers 2-0 Ayr Utd
Ayr escape conceding a third as an almighty goalmouth scramble is eventually lumped clear.
Rangers 2-0 Ayr Utd
A rare appearance for Leon King as he replaces Nico Raskin.
Rangers 2-0 Ayr Utd
Image source, SNS